Rina is a person who jokes about being addicted to caffeine or unaware that caffeine is a drug.

All people who regularly drink coffee are dependent on caffeine.

People either regularly drink coffee or joke about being addicted to caffeine.

No one who jokes about being addicted to caffeine is unaware that caffeine is a drug.

Rina is either a student and unaware that caffeine is a drug, or neither a student nor unaware that caffeine is a drug.

If Rina is not a person dependent on caffeine and a student, then Rina is either a person dependent on caffeine and a student, or neither a person dependent on caffeine nor a student.

(Student(rina) ∧ Unaware(rina)) ⊕ ¬(Student(rina) ∨ Unaware(rina))

¬(Dependent(rina) ∧ Student(rina)) → (Dependent(rina) ∧ Student(rina)) ⊕ ¬(Dependent(rina) ∨ Student(rina))


Rina is either a person who jokes about being addicted to caffeine or is unaware that caffeine is a drug.


Rina is either a person who regularly drinks coffee or a person who is unaware that caffeine is a drug.


If Rina is either a person who jokes about being addicted to caffeine and a person who is unaware that caffeine is a drug, or neither a person who jokes about being addicted to caffeine nor a person who is unaware that caffeine is a drug, then Rina jokes about being addicted to caffeine and regularly drinks coffee.


Miroslav Venhoda was a Czech choral conductor who specialized in the performance of Renaissance and Baroque music.

Miroslav Venhoda published a book in 1946 called Method of Studying Gregorian Chant.

Czech(miroslav) ∧ ChoralConductor(miroslav) ∧ Specialize(miroslav, renaissance) ∧ Specialize(miroslav, baroque)

Book(methodOfStudyingGregorianChant) ∧ Author(miroslav, methodOfStudyingGregorianChant) ∧ Publish(methodOfStudyingGregorianChant, year1946)


No choral conductor specialized in the performance of Renaissance.


If a sea eel is either an eel or a plant, then a sea eel is an eel or an animal.

Eel (seaEel) ⊕ Plant (seaEel) → Eel (seaEel) ∨ Animal (seaEel)


The Blake McFall Company Building is a commercial warehouse listed on the National Register of Historic Places.

The Blake McFall Company Building was added to the National Register of Historic Places in 1990.

The Emmet Building is a five-story building in Portland, Oregon.

The Emmet Building is another name for the Blake McFall Company Building.

∀x (Emmet(x) → Building(x) ∧ FiveStory(x) ∧ Locate(x, portland))


The Blake McFall Company Building is located in Portland, Oregon.


William Dickinson did not get a seat in the Parliament.

William Dickinson was a British politician who sat in the House of Commons

William Dickinson attended Westminster school for high school and then the University of Edinburgh.

The University of Edinburgh is a university located in the United Kingdom.

William Dickinson supported the Portland Whigs.

People who supported the Portland Whigs did not get a seat in the Parliament.

Attended(williamdickinson, westminster) ∧ Highschool(westminster) ∧ Attended(williamdickinson, universityofedinburgh)

LocatedIn(universityofedinburgh, unitedkingdom) ∧ University(universityofedinburgh)

∀x (Supported(x, portlandwhigs) → ¬SeatInParliament(x))


William Dickinson went to schools located in the United Kingdom for both high school and university.


William Dickinson attended university in the United Kingdom.


William Dickinson sat in the House of Commons.


If a universal language exists, then for every two people if they both know the same universal language they can communicate.

∀x ∀y (∃z (Know(x, z) ∧ Know(y, z) ∧ UniversalLanguage(z)) → Communicate(x, y))


All customers who are subscribed to AMC List are available to watch 3 movies every week without any additional fees.

Customers either subscribe to AMC service or HBO service.

Customers who prefer TV series more and will not watch TV series in cinemas.

All customers who subscribe to HBO services prefer TV series to movies.

∀x (PreferTVSeries(x) → ¬WatchTVInCinema(x))


James does not go to cinemas every week.


James goes to cinemas every week or watches 3 movies every week without any additional fees.


If James does not both go to cinemas every week and subscribe to HBO service, then James is either available to watch 3 movies every week without any additional fees or he prefers TV more.


If James is available to watch 3 movies every week without any additional fees and he watches TV series in cinemas, then he goes to cinemas every week and prefers TV series more.


In La Liga 2021-2022, Real Madrid ranks higher than Barcelona.

A La Liga soccer team ranks higher than another if it receives more points.

If two La Liga soccer teams recieve the same points, the team which recieves more points from the games between the two teams ranks higher.

Real Madrid and Barcelona are both La Liga soccer teams.

In La Liga 2021-2022, Real Madrid recieves 86 points and Barcelon recieves 73 points.

In La Liga 2021-2022, Real Madrid and Barcelona both recieve 3 points from the games between them.

∀x ∀y (LaLiga(x) ∧ LaLiga(y) ∧ MorePoints(x, y) → HigherRank(x, y))

∀x ∀y (LaLiga(x) ∧ LaLiga(y) ∧ ¬MorePoints(x, y) ∧ ¬MorePoints(y, x) ∧ MorePointsInGameBetween(x, y) → HigherRank(x, y))

¬MorePointsInGameBetween(realMadrid, barcelona) ∧ ¬MorePointsInGameBetween(barcelona, realMadrid)


In La Liga 2021-2022, Barcelona ranks higher than Real Madrid.


Lawton Park is a neighbourhood in Seattle.

All citizens of Lawton Park use the zip code 98199.

∀x (Citizenof(x, lawtonPark) → Usezipcode(x, number98199))


Tiffany T. Alston was suspended from the Maryland House of Delegates.

If a legislator is found guilty of stealing government funds, they will be suspended from office.

Tiffany T. Alston was a legislator in Maryland's House of Delegates from 2011 to 2013.

Tiffany T. Alston was found guilty of stealing government funds in 2012.

∀x (IsLegislator(x) ∧ StealsFunds(x) → Suspended(x))


Tiffany T. Alston was not suspended from the Maryland House of Delegates.


Tiffany T. Alston went to prison for stealing government funds.


If you step on a stonefish and don’t use an antivenom, it will cause death.

Stonefish stings cause death if not treated.

To treat stonefish stings, apply heat to the affected area or use an antivenom.

∀x (StepOn(stonefish, x) → Sting(stonefish, x))

∀x (Sting(stonefish, x) ∧ ¬Treated(x) → CauseDeath(x))

∀x (Sting(stonefish, x) ∧ (ApplyHeat(x) ∨ UseAntivenom(x)) → Treated(x))


Stings of some fish can cause death if not treated.


If you step on a stonefish and apply heat to the affected area, stings will cause death.


Some monitors produced by LG have a type-c port.

If the monitor has a type-c port, then it is not produced by AOC.

All monitors in the library are produced by AOC.

L-2021 is either in the library or has a type-c port.

L-2021 is either produced by AOC and produced by LG, or neither produced by AOC nor produced by LG.

∃x (LG(x) ∧ TypeC(x))
∀x (TypeC(x) → ¬AOC(x))
∀x (Library(x) → AOC(x))
Library(l-2021) ⊕ TypeC(l-2021)
¬(AOC(l-2021) ⊕ LG(l-2021))


L-2021 is either in the library or produced by LG.


L-2021 either has a type-c port or is produced by LG.


If L-2021 is either in the library and produced by LG, or neither in the library nor produced by LG,  then L-2021 neither has a type-c port nor is produced by LG.


If L-2021 is either produced by LG and produced by AOC or neither produced by LG nor produced by AOC,  then L-2021 is either in the library or produced by LG.


Jeremy has a busy schedule without time to cook.

People eat meat regularly or are vegetation.

If people eat meat regularly, then they enjoy eating hamburgers and steaks.

All people who are vegetarian are conscious of the environment or their health.

If people are conscious about the environment or their health, then they do not go to fast food places often.

If people have busy schedules without time to cook, then they go to fast food places often.

If Jeremy does not both go to fast food places often and is conscious about the environment or their health, then he goes to fast food places often.

¬(FastFood(jeremy) ∧ Conscious(jeremy)) → FastFood(jeremy)


Jeremy has a busy schedule without time to cook or enjoy eating hamburgers and steaks.


If Jeremy has a busy schedule without time to cook or enjoy eating hamburgers and steaks, then Jeremy neither has a busy schedule without having time to cook nor enjoys eating hamburgers and steaks.


The project Sam is doing is written in C++.

A project is written either in C++ or in Python.

If Sam does a project written in Python, he will not use a Mac.

If a song is not "Perfect", Sam will never play it.

∀x (Project(x) → (WrittenIn(x, python) ⊕ WrittenIn(x, c++)))

∀x (Project(x) ∧ WrittenIn(x, python) ∧ Do(sam, x) → ¬Use(sam, mac))

Use(sam, mac) → ∃x (Song(x) ∧ Play(sam, x))


If a song is "Perfect", Sam will play it.


All rabbits have fur
Some pets are rabbits.

∀x (Rabbit(x) → HasFur(x))
∃x (Pet(x) ∧ Reptile(x))


All YouTube-related applications are video applications.

An APP is either related to YouTube or Instagram.

If something is interesting, then it is good.

∀x (App(x) → Software(x))
∀x (Youtube(x) → App(x))
∀x (Youtube(x) ∨ Instagram(x))
∀x (Instagram(x) → Entertainment(x))
∀x (Software(x) → Program(x))
∀x (Entertainment(x) → Interesting(x))
∀x (Interesting(x) → Good(x))
¬Good(tiktok)


Tiktok is not both related to youtube and a program.


Tiktok is either related to youtube or a program.


There are no unincorporated communities along Kentucky Route 32.

Ordinary is an unincorporated community.

Located within Elliot County, Ordinary is on Kentucky Route 32.

Ordinary is located northwest of Sandy Hook.

In(ordinary, elliotcounty) ∧ On(ordinary, kentuckyroute32)


There is an unincorporated community in Elliot County.


Someone is either a Yale student or a Harvard student.

If Susan is a Harvard student, then she is a young adult.

If Susan is a Yale student, then she does not go on a diet.


Susan does not go on a diet and is diligent.


The only style of music Vic DiCara plays is punk music.

Vic DiCara played in the band Inside Out.

Play(vicdicara, guitar) ∧ Play(vicdicara, bass)

¬(∃x (Music (vicdicara, punk) ∧ Music (vicdicara, x)))


All Olympic gold medal winners are good athletes.

Amy is good at sports or Amy is an Olympic gold medal winner.

If Amy is not a Nobel laureate, then Amy is not an Olympic gold medal winner.

∀x (OlympicGoldMedalWinner(x) → Athlete(x))


Amy is neither a scientist nor an Olympic gold medal winner.


If Amy is not an Olympic gold medal winner, then Amy is a Nobel laureate.


All fruits with the color red contain a large amount of vitamin C.

All apples are fruits with the color red.

All fruits containing a large amount of vitamin C are beneficial to people.

No fruits that are beneficial to people are on a warning list.

If K is not beneficial to people and also not an apple, then it is a fruit with the color red.

∀x (RedFruit(x) → VC(x))
∀x (Apple(x) → RedFruit(x))
∀x (VC(x) → Benefit(x))
∀x (Benefit(x) → ¬WarningList(x))
¬(Benefit(k) ∧ Apple(k)) → RedFruit(k)


K either contains a large amount of vitamin C or is on a warning list.


K is either on a warning list or with the color red.


If K is either beneficial to people or on a warning list, then it is not red.


If K is either on a warning list or with the color red, then it is not beneficial to people and does not contain a large amount of vitamin C.


Everyone working at Meta has a high income.

If a person has a high income, then he/she will not take a bus to their destination.

People will either take a bus or drive to their destination.

Everyone who has a car will choose to drive to their destination.

∀x (Meta(x) → HighIncome(x))
∀x (HighIncome(x) → ¬Bus(x))
∀x (Bus(x) ∨ Drive(x))
∀x (HaveCars(x) → Drive(x))
∀x (Student(x) → ¬Drive(x))
HaveCars(james) ∨ Meta(james)


James drives to his destination or he is a student.


James either drives to their destination or is a student.


If James either drives to his destination or is a student, then he has a high income and is a student.


Students either go to the park or go to the movies.

No student who enjoys nature has free time during the weekend.

All students who go to the movies enjoy nature.

All students who do not have class during the weekend have free time during the weekend.

All students not in summer camp do not have class during the weekend.

James does not have class during the weekend.

∀x (Park(x) ⊕ Movies(x))
∀x (Nature(x) → ¬FreeTime(x))
∀x (Movies(x) → Nature(x))
∀x (NoClass(x) → FreeTime(x))
∀x (SummerCamp(x) → NoClass(x))
NoClass(james)


James goes to the park or is in summer camp.


All television stars have good business sense.

No television stars are certified public accountants.

All certified public accountants have good business sense.

∀x (TelevisionStar(x) → ¬CertifiedPublicAccoutant(x))

∀x (CertifiedPublicAccoutant(x) → GoodBusinessSense(x))


Some students good at math are good at chemistry.

All students good at chemistry enjoy conducting experiments.

All students that enjoy conducting experiments are good at planning.

No student good at planning is awarded the Dean's List.

James is either good at chemistry and awarded the Dean's List, or neither good at chemistry nor awarded the Dean's List.

∃x (Math(x) ∧ Chemistry(x))
∀x (Chemistry(x) → Experiment(x))
∀x (Experiment(x) → Planning(x))
∀x (Planning(x) → ¬Award(x))
¬(Chemistry(james) ⊕ Award(james))


James is either good at planning or good at math.


James is either good at chemistry or good at math.


If James is good at Chemistry or gets awarded the Dean's List, then James is either good at planning or good at math.


2Sum is a Leetcode problem with an easy level.

If a Leetcode problem is at the easy level, then its AC rate is lower than 20 percent.

All Leetcode problems that are recommended to novices are easy.

A Leetode problem is either easy or hard.

Leetcode problems that are starred by more than 1 thousand users are hard.

4Sum is starred by more than 1 thousand users.

∀x (Easy(x) → LowerAC(x))
∀x (Recommended(x) → Easy(x))
∀x (Easy(x) ⊕ Hard(x))
∀x (Starred(x) → Hard(x))
Recommended(twosum)
Starred(foursum)


4Sum is a Leetcode problem recommended to the novice.


2Sum has an AC rate higher than 20 percent.


Whenever Sarah goes to Vermont, Sarah drives there.

For someone who does not own a car to drive somewhere, they must either borrow a car or rent a car.

Sarah never borrows a car to go camping.

Sarah is going to go camping in Vermont this weekend.

To go camping somewhere, you must go to that place.

GoesTo(sarah, vermont) → DriveTo(sarah, vermont)

∀x ∀y (¬Own(x, car) ∧ DriveTo(x, y) → Borrow(x, car) ⊕ Rent(x, car))

∀x (Camping(sarah, x) → ¬(Borrow(sarah, car)))


All people who attend weddings are getting married or have friends who are getting married.

No preteens and other young children are getting married or have friends who are getting married.

If people enjoy celebrating life milestone events with other people, then they attend weddings.

If people are fond of large organized group functions, then they enjoy celebrating life milestone events with other people.

All people who are outgoing and very spirited are fond of large organized group functions.

If Carol is not both a pre-teen or other young child and attends weddings, then Carol is not getting married or has friends who are getting married.

¬(PreTeen(Carol) ∧ Weddings(Carol)) → ¬GettingMarried(Carol)


Carol is either a preteen or other young child.


Carol neither enjoys celebrating life milestone events with other people nor is outgoing and very spirited.


A U.S government official is a Democrat.

A U.S government official is either conservative or a Republican.


A U.S government official is anti-abortion and a liberal.


A U.S government official is either anti-abortion or a liberal.


If a U.S government official is not anti-abortion and a Republican, then a U.S government official is neither anti-abortion nor a liberal.


If a U.S government official is anti-abortion and a liberal, then a U.S government official is either a Republican or a liberal.


If a U.S government official is either a conservative or anti-abortion, then a U.S government official is either a conservative and a liberal or neither a conservative nor a liberal.


If a U.S government official is either a conservative or anti-abortion, then a U.S government official is neither a Democrat or a liberal.


If an U.S government official is anti-abortion or a liberal, then a U.S government official is either anti-abortion or a liberal.


Some conservatives are advocates of high tariff rates.

All advocates of high tariff rates are Republicans.

∀x (AdvocateOfHighTariff(x) → Republican(x))


All professional basketball players are athletes.

All NBA players are professional basketball players.

Jim is either not a professional basketball player or not a slow runner.

∀x (ProfessionalBasketballPlayer(x) → Athlete(x))

∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))


If someone loves animals, then they are not bad.

If Nancy is not a pirate, then Nancy loves animals.

If Nancy is not a toddler, then Nancy is bad.

∀x (Kid(x) → LoveAnimals(x))
∀x (Toddler(x) → Kid(x))
∀x (LoveAnimals(x) → ¬Bad(x))
∀x (Pirate(x) → Bad(x))
¬Pirate(nancy) → LoveAnimals(nancy)
¬Toddler(nancy) → Bad(nancy)


If Nancy is not a pirate or a toddler, then she loves animals and is a kid.


Lana Wilson directed After Tiller, The Departure, and Miss Americana.

If a film is directedy by a person, the person is a filmmaker.

If a person is from a city in a country, the person is from the country.

After Tiller is nominated for the Independent Spirit Award for Best Documentary.

DirectedBy(after_Tiller, lana_Wilson) ∧ DirectedBy(the_Departure, lana_Wilson) ∧ DirectedBy(miss_Americana, lana_Wilson)

∀x ∀y ∀z (FromCity(x, y) ∧ CityCountry(y, z) → FromCountry(x, z))


Miss Americana is not directed by a filmmaker from Kirkland.


Lana Wilson has won the Independent Spirit Award.


All bears in zoos are not wild.
Some bears are in zoos.

∀x ((Bear(x) ∧ InZoo(x)) → ¬Wild(x))
∃x (Bear(x) ∧ InZoo(x))


If a person is the leader of a country for life, that person is in a monarchy.

∀x (Leader(x) → InMonarchy(x))
∀x (Leader(x) → King(x) ⊕ Queen(x))
∀x (Queen(x) → Female(x))
∀x (King(x) → Male(x))
Queen(elizabeth)
Leader(elizabeth)


If people make their own matcha teas every morning with ceremonial-grade matcha powder, then they do not wake up late and start their schedules past noon regularly.

If people live in California and attend yoga classes regularly, then they make their own matcha teas every morning with ceremonial-grade matcha powder.

If people work in the entertainment industry as high-profile celebrities, then they wake up late and start their schedules past noon regularly.

If people do not have regular 9-5 jobs, then they work in the entertainment industry as high-profile celebrities.

All people who prefer working at home over going to the office every day do not have regular 9-5 jobs.

Clay either both prefers to work at home over going to the office every day and makes his own matcha teas every morning with ceremonial-grade matcha powder, or he neither prefers to work at home over going to the office every day nor makes his own matcha teas every morning with ceremonial-grade matcha powder.

(WorkHome(clay) ∧ Matcha(clay)) ⊕ (¬WorkHome(clay) ∧ ¬Matcha(clay))


Clay lives in California and attends yoga classes regularly.


Clay neither prefers working at home over going to the office every day nor lives in California and attends yoga classes regularly.


Thomas Barber played in the Football League for Bolton Wanderers

Thomas Barber was an English professional footballer.

Thomas Barber played in the Football League for Aston Villa.

Thomas Barber played as a half back and inside left.

Thomas Barber scored the winning goal in the 1913 FA Cup Final.

PlayedAs(thomasBarber, aHalfBack) ∧ PlayedAs(thomasBarber, anInsideLeft)


An English professional footballer scored the winning goal in the 1913 FA Cup Final.


If people play the instrument in the concert, then he is good at playing this kind of instrument.

Peter plays piano, violin, and saxophone.

Peter was invited to play piano at the concert hall.

Oliver and Peter were both invited to perform in the concert.

Oliver plays a different musical instrument from Peter in the concert.

∀y (∀x (PlayInConcert(y, x) → GoodAt(y, x)))


If something can go underwater, then it enjoys water.

All animals that can swim can go underwater.

Either an animal can swim or it can walk.

Animals that enjoy water splash water around.

Every animal that travels on land enjoys basking in the sun.

George splashes water around and can swim.

Liam is either an animal that can walk and enjoys water, or is neither an animal that can walk nor enjoys water.

∀x (TravelsOnLand(x) → EnjoysBasking(x))

(CanWalk(liam) ∧ EnjoysWater(liam)) ∨ (¬CanWalk(liam) ∧ ¬EnjoysWater(liam))


Liam enjoys basking in the sun and splashing water around.


Liam neither enjoys basking in the sun nor splashing water around.


Cancer researchers tend to use the cancer effect size to determine the relative importance of the genetic alterations that confer selective advantage to cancer cells.

Cancer biology is finding genetic alterations that confer selective advantage to cancer cells.

Cancer researchers have frequently ranked the importance of substitutions to cancer growth by P value.

P values are thresholds for belief, not metrics of effect.

∀x (PValue(x) → ThresholdsForBelief(x) ∧ ¬MetricsOfEffect(x))


P value represents the selection intensity for somatic variants in cancer cell lineages.


Cancer effect size is a metric that is preferred by the majority of cancer researchers.


P value doesn't represent metrics of effect.


All dispensable things are environment-friendly.

All environment-friendly things are good.

A worksheet is either paper or is environment-friendly.

∀x (Dispensable(x) → EnvironmentFriendly(x))


No reptile has fur.
All snakes are reptiles.

∀x (Reptile(x) → ¬HasFur(x))
∀x (Snake(x) → Reptile(x))


All buildings managed by the Yale Housing are located in New Haven.

All buildings owned by Bloomberg are located in Manhattans.

All buildings with the Bloomberg logo are owned by Bloomberg.

∀x (YaleHousing(x) → Located(newhaven, x))

∀x (Bloomberg(x) → Located(manhattans, x))


Either an animal is a bird or it eats other animals.

If an animal eats other animals, then it is a carnivore.

Ron is neither a cold-blooded animal nor a carnivore.

Henry is neither a carnivore nor a lizard.

∀x (ColdBlooded(x) → ¬Bird(x))
∀x (Reptile(x) → ColdBlooded(x))
∀x (Bird(x) ∨ EatOtherAnimals(x))
∀x (EatOtherAnimals(x) → Carnivore(x))
¬ColdBlooded(ron) ∧ ¬Carnivore(ron)
¬Carnivore(henry) ∧ ¬Lizard(henry)


Either Henry is a reptile or Ron eats other animals.


It is not true that Ron is a reptile or that Henry is cold-blooded.


Yevgeny Kurochkin discovered a new bird genus.

Ambiorus Dementjevi is the only known species of Ambiortus.

The Mongol region was where Ambiorus Dementjevi lived.

Yevgeny Kurochkin was the discoverer of Ambiortus.

∀x (Species(x, ambiortus) → AmbiortusDementjevi(x))

∀x (AmbiortusDementjevi(x) → Lived(x, mongolregion))


There is a species of Ambiortus that doesn't live in the Mongol region.


Yevgeny Kurochkin lived in the Mongol region.


All species of Ambiortus live in the Mongol region.


Everyone that uses a football can throw a football.

If someone plays football, then they use a football.

Either someone is a football player or a basketball player.

Everyone that can throw a football can throw a football with a spiral.

If someone is tall, then they are in shape.

If Jack is neither tall nor a basketball player,  then Jack is neither tall nor can throw a football.

∀x (BasketballPlayer(x) ∨ PlayFootball(x))

∀x (ThrowFootball(x) → ThrowFootballSpiral(x))

¬Tall(jack) ∧ ¬BasketballPlayer(jack) → ¬Tall(jack) ∧ ¬ThrowFootball(jack)


Pierre de Rigaud de Vaudreuil built a fort in New France.

Fort Ticonderoga is the current name for Fort Carillon.

Pierre de Rigaud de Vaudreuil built Fort Carillon.

Fort Carillon was located in New France.


Pierre de Rigaud de Vaudreuil built a fort in New England.


No soccer players are professional basketball players.

All NBA players are professional basketball players.

If Stephen Curry is an NBA player or a soccer player, then he is a professional basketball player.

¬(∃x (SoccerPlayer(x) ∧ ProfessionalBasketballPlayer(x)))

∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))

(NBAPlayer(stephencurry) ⊕ SoccerPlayer(stephencurry)) → ProfessionalBasketballPlayer(stephencurry)


Stephen Curry is not a centerback player.


Mac is neither a folk song nor a sci-fi movie.

∀x (Song(x) → ¬Visual(x))
∀x (FolkSong(x) → Song(x))
∀x (Video(x) → Visual(x))
∀x (Movie(x) → Video(x))
∀x (ScifiMovie(x) → Movie(x))
ScifiMovie(inception)
¬FolkSong(mac) ∧ ¬ScifiMovie(mac)


Inception is either a video or a folk song.


People are either extroverts or introverts.

If someone is an introvert, then they are shy and reticent.

No shy and reticent person likes to talk to strangers.

Jeff is not an extrovert and someone who likes to talk to strangers.

∀x (Extroverts(x) → OvertlyExpressive(x))

∀x (Introverts(x) → ShyAndReticentPerson(x))

∀x (ShyAndReticentPerson(x) → ¬LikeToTalkToStrangers(x))


Jeff is overtly expressive and likes to talk to strangers.


If Jeff is either overtly expressive and likes to talk to strangers or neither overtly expressive nor likes to talk to strangers, then Jeff is neither an extrovert nor likes to talk to strangers.


No low-scoring players are top players in the league.

Basketball players are either top players in the league or successfully shoot a high percentage of 3-pointers.

All players who successfully shoot a high percentage of 3-pointers are solid at shooting 2-pointers.

No players who are solid at shooting 2-pointers are bad at mid-range shots.

Candace is either a low-scoring player or successfully shoots a high percentage of 3-pointers.


Candace is solid at shooting 2-pointers or bad at mid-range shots.


Candace is either solid at shooting 2-pointers or bad at mid-range shots.


Candace is a low-scoring player or bad at mid-range shots.


Candace is either a low-scoring player or bad at mid-range shots.


Candace is either a player who successfully shoots a high percentage of 3-pointers or is bad at mid-range shots.


If Candace is not solid at shooting 2-pointers and bad at mid-range shots, then Candace is not solid at shooting 2-pointers and is a player who successfully shoots a high percentage of 3-pointers.


If Candace is solid at shooting 2-pointers or successfully shoots a high percentage of 3-pointers, then Candace is a top player in the league and bad at mid-range shots.


No plants are fungi.
Mushrooms are fungi.

∀x (Plant(x) → ¬Fungi(x))
∀x (Mushroom(x) → Fungi(x))


No road is clean.
And some streets are roads.

∀x (Road(x) → ¬Clean(x))
∃x (Street(x) ∧ Road(x))


Some people flying from New York City to Seattle will be uncomfortable.

If a person from a city on the East coast is traveling to a city on the west coast, they will be on a long flight.

Most passengers on flights to Seattle from New York City are not in first class.

People on long flights are uncomfortable unless they're in first class

∀x ∀y ∀z ((TravelingFrom(x, y) ∧ On(y, eastcoast) ∧ TravelingTo(x, z) ∧ On(z, westcoast)) → OnLongFlight(x))

∃x (¬InFirstClass(x) ∧ TravelingFrom(x, newyorkcity) ∧ TravelingTo(x, seattle))

∀x (OnLongFlight(x) ∧ ¬InFirstClass(x) → Uncomfortable(x))


If a musician is not famous, that musician will not make a lot of money.

∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeMoney(x))

∃x (Musician(x) ∧ Singer(x) ∨ Writer(x))


Each building is tall.
Everything tall has  height.

∀x (Building(x) → ¬Tall(x))
∀x (Tall(x) → HasHeight(x))


The main character of the film Garfield is childish and possessive.

A cat named Garfield, which is the main character of the film Garfield, is orange and fat and likes having lasagna.

Garfield and Odie, who is another pet of Jon, share the same home.

A pet who hates the pet with whom he shares the same owner is childish and possessive.

Cat(garfield) ∧ MainCharacterGarfield(garfield) ∧ BeOrange(garfield) ∧ BeFat(garfield) ∧ LikeLasagna(garfield)

Pet(garfield, jon) ∧ Pet(odie, jon) ∧ ShareHome(garfield, odie)

∀x ∀y ∃z (Pet(x, z) ∧ Pet(y, z) ∧ Hate(x, y) → BeChildish(x) ∧ BePossessive(x))


If something eats, then it is not a plant.

∀x (Human(x) → Eat(x))
∀x (Eat(x) → ¬Plant(x))
∀x (Plant(x) ∨ Animal(x))
∀x (Goat(x) → Animal(x))
∀x (Dirt(x) → ¬Animal(x))
Goat(hulu) ∨ Human(hulu)


If Hulu is either an animal or dirt, then Hulu eats and is dirt.


The Controlled Substances Act prevents harmful things.

There exist both harmful and beneficial controlled substances.

If a child is exposed to a controlled substance, he or she is in chemical endangerment.

The Controlled Substances Act was an act passed in 1971.

∃x ∃x (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ Beneficial(x) ∧ Harmful(y))

∀x ∀y (ExposedToControlledSubstance(x, y) → ChemicalEndangerment(x))

∀x (ChemicalEndangerment(x) → Harmful(x))

PassedIn(controlledSubstancesAct, year1971) ∧ Act(controlledSubstancesAct)


A child in chemical endangerment is in harm.


No people who work at corporate jobs are starting a new company.

All entrepreneurs are starting a new company.

All risk-averse people are people who work at corporate jobs.

All people who hate working for others are entrepreneurs.

If Mark Zuckerberg is neither an entrepreneur nor a person who hates working for others, then Mark Zuckerberg is not a risk-averse person.

∀x (WorkAtCorporateJobs(x) → ¬StartingANewCompany(x))

∀x (Entrepreneurs(x) → StartingANewCompany(x))

∀x (Risk-averse(x) → WorkAtCorporateJobs(x))

∀x (HateWorkingForOthers(x) → Entrepreneurs(x))

¬Entrepreneurs(markZuckerberg) ∨ ¬HateWorkingForOthers(markZuckerberg) → ¬Risk-averse(markZuckerberg)


Mark Zuckerberg is a risk-averse person.


Mark Zuckerberg is not a risk-averse person.


If someone is cooking downstairs, it will always cause the first floor to become smokey.

There are two kitchens in the house: the upstairs kitchen and the downstairs kitchen.

When someone is cooking in the downstairs kitchen, the first floor becomes smokey unless the air conditioner is running.

If the air conditioner is running and someone is cooking in the downstairs kitchen, all the smoke travels to the second floor.

(Cook(downstairs) ∧ ¬Run(ac)) → Smokey(firstFloor)

(Cook(downstairs) ∧ Run(ac)) → Smokey(secondFloor)


If someone is cooking upstairs, the first floor will become smokey.


If someone is cooking downstairs and the air conditioner is running, there will be smoke upstairs.


A highly developed city is located in the western hemisphere of the earth.

New York City is Located in the United States of America.

United States of America is part of North America.

North America is in the western hemisphere of the earth.

New York City is a highly developed city.

If place A is located in place B and place B is located in place C, then place A is located in place C.

∀x ∀y ∀z ((Locate(x, y) ∧ Locate(y, z)) → Locate(x, z))


USA is not located in western hemisphere of the earth.


New York City is located in the New York State.


There exists a poem written by an ancient Roman writer with a strong analogy of human aging.

Callus 4 is a poem that was written by the ancient Roman writer Catullus.

Callus 4 is a story about the retirement of a well-traveled ship.

There is a strong analogy of human aging in the poem Callus 4.

Callus 4 is written in an unusual iambic trimeter to convey a sense of speed over the waves.

Poem(callus4) ∧ WrittenBy(callus4, catullus) ∧ Roman(catullus)

Poem(callus4) → Lambic(callus4) ∧ Waves(callus4)


There exists a poem written by an ancient Roman writer written in iambic petameter.


Callus 4 is written in an unusual iambic trimeter to convey a strong analogy of human aging.


Michael Crichton has directed a film about robots.

Westworld is an American science fiction-thriller TV series.

In 2016, a new television series named Westworld debuted on HBO.

The TV series Westworld is adapted from the original film in 1973, which was written and directed by Michael Crichton.

The 1973 film Westworld is about robots that malfunction and begin killing the human visitors.

TVSeries(westworld) ∧ American(westworld) ∧ ScienceFictionThriller(westworld)

∃x (Adapt(westworld, x) ∧ Produce(x, year1973) ∧ Write(michael, x) ∧ Direct(michael, x))


Russia did not win fewer gold medals than China.

The 2008 Summer Olympics were held in Beijing, China.

The 2008 Summer Olympics were the second Summer Olympic Games to be held in a communist state.

China won the most gold medals (48) in the 2008 Summer Olympics.

The United States placed second in the gold medal tally but won the highest number of medals overall (112) in the 2008 Summer Olympics.

The third place in the gold medal tally was achieved by Russia in the 2008 Summer Olympics.

If a country places third in gold medals, then they had fewer gold medals than the team that won the most gold medals.

87 countries won at least one medal during the 2008 Games.

Placed(unitedstates, secondingoldmedals) ∧ Won(unitedstates, highestnumberofmedals)

∀x ∀y (Placed(x, thirdingoldmedals) ∧ Won(y, mostgoldmedals) → FewerGoldMedalsThan(x, y))


The United States won fewer gold medals than China.


Russia won fewer gold medals than China.


Xiangshan and Diecai are districts in the same city.

Xiufeng, Xiangshan, Diecai, Qixing are districts in the city of Guilin.

DistrictIn(xiufeng, guilin) ∧ DistrictIn(xiangshan, guilin) ∧ DistrictIn(diecai, guilin) ∧ DistrictIn(qixing, guilin) ∧ City(guilin)


Michael enjoys going out often to restaurants with friends.

All people who grow their own fresh vegetables in their home garden also have ample space.

If people are young working professionals who live in large cities, then they do not have ample space.

If people order takeout from delivery services often, then they grow their own fresh vegetables in their home garden.

If people enjoy going out often to restaurants with friends, then they order takeout from delivery services often.

If people regularly tout the benefits of homegrown and homecooked meals over fast food, then they enjoy going out often to restaurants with friends.

Michael grows his own fresh vegetables in his home garden or regularly touts the benefits of homegrown and homecooked meals over fast food.

∀x (Garden(x) → Space(x))
∀x (Professional(x) → ¬Space(x))
∀x (Takeout(x) → Garden(x))
∀x (GoingOut(x) → Takeout(x))
∀x (Homecooked(x) → GoingOut(x))
Garden(michael) ∨ Homecooked(michael)


Michael is a young working professional who lives in large cities.


Michael grows his own fresh vegetables in their home garden or is a young working professional who lives in large cities.


All devices belonging to the company are connected to Google Home.

All devices belonging to employees are connected to the company's wifi.

All devices connected to Google Home are controlled by the managers.

All devices that connect to the company's wifi are easy to operate.

∀x (Company(x) → GoogleHome(x))
∀x (Employee(x) → Wifi(x))
∀x (GoogleHome(x) → Controlled(x))
∀x (Wifi(x) → EasyToOperate(x))
Employee(iPod1)


Ryan is interesting as an individual performer.

No touring musicians are permanent members of an orchestra.

Musicians are either permanent members of an orchestra or have a unique musical voice or style.

All musicians who have a unique musical voice or style are interesting as individual performers.

All musicians who are interesting as individual performers are capable of attracting large audiences.

If Ryan is interesting as an individual performer and has a unique musical voice or style, then Ryan is either a touring soloist musician and capable of attracting large audiences, or neither a touring soloist musician nor capable of attracting large audiences.

(Interesting(ryan) ∧ Unique(ryan)) → ¬(Touring(ryan) ⊕ Capable(ryan))


Ryan is either a permanent member of an orchestra or a touring soloist musician.


Ryan is either a permanent member of an orchestra or has a unique musical voice or style.


If someone yells, then they are not cool.

Harry either yells and flies, or neither yells nor flies.

(Yell(harry) ∧ Fly(harry)) ⊕ (¬Yell(harry) ∧ ¬Fly(harry))


Products are either produced in China or the US.

All produced in the US are sold in the US.

If labeled, then the product is cheaper.

All displayed on the homepage are sold in Walmart.

No products returned by customers are sold in Walmart.

G-910 is either displayed on the homepage or cheaper.

∀x (DisplayedInHomepage(x) → SoldInWalmart(x))

∀x (ReturnedByCustomer(x) → ¬SoldInWalmart(x))


G-910 is a product returned by customers.


G-910 is a product returned by customers or sold in Walmart.


G-910 is either returned by customers or sold in Walmart.


Marcy either orders a lot of Amazon packages or saves a lot of money.

People either order a lot of Amazon packages or are environmentally conscious.

If people order a lot of Amazon packages, then they get a lot of daily mail delivered.

If people are environmentally conscious, then they have solar panels in their homes.

If people get a lot of daily mail delivered, then they are very involved with their neighborhood.

If people have solar panels in their homes, then they save a lot of money.

If Marcy either gets a lot of mail and is very involved with her neighborhood or if she does not order a lot of Amazon packages nor is very involved with her neighborhood, then Marcy does not both get a lot of daily mail and order a lot of Amazon packages.

¬(DailyMail(marcy) ⊕ Neighborhood(marcy)) → (¬DailyMail(marcy) ∨ ¬Amazon(marcy))


If Marcy is not a person who orders a lot of Amazon packages and is very environmentally conscious, then Taylor is not someone who saves a lot of money and is environmentally conscious.


When the police complete investigations, the prosecutor will prosecute the offender at an appropriate court.

In Indonesia, the prosecutor only personally investigates cases of some special crimes.

Once the police complete investigations of a crime, they hand the evidence to the prosecutor.

Evidence can be either satisfactory or unsatisfactory.

If the police hand the evidence to the prosecutor and the evidence is satisfactory, the prosecutor will prosecute the offender in an appropriate court.

∃x ∃y (Country(indonesia) ∧ Prosecutor(x) ∧ Crime(y) → InvestigatePersonally(x, y))

∀x ∀y (Crime(y) ∧ PoliceCompInves(y) ∧ Prosecutor(x) → Evidence(y) ∧ HandToProsecutor(x, y))

∀x (Crime(x) ∧ Evidence(x) ∧ (Satisfactory(x) ⊕ Unsatisfactory(x)))

∀x ∀y (Evidence(y) ∧ HandToProsecutor(x, y) ∧ Satisfactory(y) → ProsecuteTheOffender(x, y))


In Indonesia, the prosecutor personally investigates cases of corruption.


When the police complete investigations, the prosecutor investigates in personally.


No watch that is battery-powered is automatic.

All digital watches are battery-powered.

Moonwatch is not a digital watch or an automatic.

∀x (BatteryPoweredWatch(x) → ¬AutomaticWatch(x))

∀x (DigitalWatch(x) → BatteryPoweredWatch(x))

∃x (MechanicalWatch(x) ∧ AutomaticWatch(x))


Moonwatch is a smartwatch and a mechanical watch.


If Moonwatch is a smartwatch and a mechanical watch, then Moonwatch is not a mechanical watch.


If Moonwatch is a mechanical or battery-powered watch, then Moonwatch is not a smartwatch.


John cannot use different condiments to cook.

If a person can distinguish the taste of different condiments, then he/she can also use different condiments to cook.

People who have the talent of cooking can distinguish the taste of different condiments.

Only people with the talent of cooking can make delicious meals.

If the meal is popular at the party, then it is delicious.

John can make meals which are popular at the party.

∀x (People(x) ∧ DistinguishCondiments(x) → UseDiffCondiments(x)) ∧ (∃x (People(x) ∧ ¬DistinguishCondiments(x) ∧ UseDiffCondiments(x))) ∧ ¬(∀x (People(x) ∧ DistinguishCondiments(x)))

∀x (People(x) ∧ TalentCooking(x) → DistinguishCondiments(x))

∀x ∀y (MakeMeal(x, y) ∧ Delicious(y) ∧ People(x) → TalentCooking(x))

∀x ∀y (MakeMeal(x, y) ∧ People(x) ∧ Popular(y) → Delicious(y))

∃x (People(john) ∧ MakeMeal(john, x) ∧ Popular(x) ∧ People(peter) ∧ ¬UseDiffCondiments(peter))


In Russia, an effective monetary policy is possible.

Effective monetary policy is possible with successful inflation control and a strong national currency.

A country cannot simultaneously regulate the exchange rate and successfully control inflation.

The introduction of an embargo on foreign trade goods in a country leads to a sharp decrease in exports.

If exports fall sharply, the national currency cannot be in this country.

Regulation of the exchange rate is required to have a strong national currency.

There is an embargo on Russian foreign trade goods.

∀x (EffMonPolicy(x) → InfControl(x) ∧ StongCurr(x))


Viewers send in funny videos to the French broadcast channel that are in French.

Video Gag is a French television series that airs weekly.

Video Gag airs on the French broadcast channel TF1.

If viewers send in funny videos to the French broadcast channel, then Video Gag airs them on television.

All videos aired on Video Gag are in French.

∀x (VideoGag(x) → FrenchTelevision(x) ∧ AirsWeekly(x))

∀x (VideoGag(x) → AirsWeekly(x) ∧ French(x))


Viewers send in funny videos to the French broadcast channel that are in English.


All phones are things.
All cellphones are phones.
All iPhones are cellphones.
All engineers are workers.
All workers are human.
Jack is either an engineer or a worker.
Jack is is either a human or a phone.

∀x (Phone(x) → Thing(x))
∀x (Cellphone(x) → Phone(x))
∀x (Iphone(x) → Cellphone(x))
∀x (Engineer(x) → Worker(x))
∀x (Worker(x) → Human(x))
Engineer(jack) ⊕ Worker(jack)
Human(jack) ⊕ Phone(jack)


All iPhones are electronic.
Some phones are iPhones.

∀x (IPhone(x) → Electronic(x))
∃x (Phone(x) ∧ IPhone(x))


A museum in NYC includes Byzantine and Islamic Art.

Metropolitan Museum of Art is a museum in NYC.

Whitney Museum of American Art is a museum in NYC.

Museum of Modern Art (MoMA) is a museum if NYC.

Metropolitan Museum of Art includes Bytantine and Islamic Art.

Whitney Museum of American Art includes American art.

Include(metropolitanMuseumofArt, byzantineArt) ∧ Include(metropolitanMuseumofArt, islamicArt)


Benji is a person who likes eating cheese.

A person either likes eating cheese or is a francophile.

No francophiles are people who like Spain as their favorite country.

A person likes Spain as their favorite country or likes eating cheese.

Benji is not a person who likes eating cheese and a person who studies Spanish.

If Benji is neither a person who studies Spanish nor a person that studies French, then Benji is a person who studies Spanish or a person that studies French.

¬(Spanish(benji) ∨ French(benji)) → ¬(Cheese(benji) ⊕ French(benji))


If Benji is either a person who likes eating cheese or a francophile, then Benji is neither a person who studies Spanish nor a person who studies French.


If Benji is a person who likes Spain as their favorite country or studies French, then Benji is either a person who studies Spanish or a person who likes Spain as their favorite country.


Gasteren is village located in the province of Drenthe.

The population of a village in Drenthe was 155 people.

Village(gasteren) ∧ Province(drenthe) ∧ LocatedIn(gasteren, drenthe)

∃x (Population155(x) ∧ Village(x) ∧ LocatedIn(x, drenthe))


The only types of mammals that lay eggs are platypuses and echidnas.

All animals are either vertebrates or invertebrates.

Grebes are not platypuses and also not echidnas.

∀x ((Mammal(x) ∧ LayEgg(x)) → (Platypuses(x) ⊕ Echidnas(x)))

∀x (Animal(x) → Invertebrate(x) ⊕ Vertebrate(x))

∀x (Grebes(x) → (¬Platypuses(x) ∧ ¬Echidnas(x)))


Bobby Flynn finished 7th while competing on Australian Idol.

Australian Idol competitors are Australian citizens.

The Omega Three band made a nationwide tour in 2007.

Bobby Flynn is a member of The Omega Three band.

∀x (CompetedOnAustralianIdol(x) → AustralianCitizen(x))


All proteins are organic compounds.
All enzymes are organic compounds.

∀x (Protein(x) → OrganicCompound(x))
∀x (Enzyme(x) → OrganicCompound(x))


There is a series by ABC that was developed by the showrunner of Witches of East End.

One American screenwriter and producer is Maggie Friedman.

Maggie Friedman was the showrunner and executive producer of the lifetime television series Witches of East End.

Witches of East End is a fantasy-drama series.

Maggie Friedman produced and developed Eastwick.

American(maggiefriedman) ∧ Screenwriter(maggiefriedman) ∧ Producer(maggiefriedman)

ShowRunnerOf(maggiefriedman, witchesofeastend) ∧ ExecutiveProducerOf(maggiefriedman, witchesofeastend) ∧ LifetimeTelevisionSeries(maggiefriedman)

Produced(maggiefriedman, eastwick) ∧ Developed(maggiefriedman, eastwick)


There isn't a series by ABC that was developed by the showrunner of Witches of East End.


Maggie Friedman developed Witches of East End.


Evangelos Eleftheriou is a Greek electrical engineer.

Evangelos Eleftheriou worked for IBM in Zurich.

If a company has employees working for them somewhere, then they have an office there.

WorkedFor(evangeloseleftheriou, ibm) ∧ WorkedIn(evangeloseleftheriou, zurich)

∀x ∀x ∀z (Company(x) ∧ WorkedFor(y, x) ∧ WorkedIn(y, z) → HasOfficeIn(x, z))


"Hooray! Hooray! It's a Holi-Holiday!" was a #1 hit in Germany.

Before releasing their single, "Hooray! Hooray! It's a Holi-Holiday!", Boney M. had had seven consecutive German #1 singles.

"Hooray! Hooray! It's a Holi-Holiday!" was a big hit all over Europe.

Nevertheless, "Hooray! Hooray! It's a Holi-Holiday!" broke Boney M's streak of consecutive German #1 singles.

A song that peaks below #1 on the german charts is also a song that is not the #1 single

∃x (Song(x) ∧ By(x, boneym) ∧ N1GermanSingle(x))

∀x (PeaksBelowN1(x) ↔ ¬N1GermanSingle(x))


"Hooray! Hooray! It's a Holi-Holiday!" peaked below #1 on the German charts.


"Hooray! Hooray! It's a Holi-Holiday!" peaked at #3 on the UK charts.


People who cook can make scrambled eggs and pasta.

If someone can make cookies and muffins, they are a baker.

Bakers who can also make scrambled eggs can make a good breakfast.

Luke can make cookies, scrambled eggs, and muffins, but not pasta.

∀x (Cook(x) → (MakeScrambledEggs(x) ∧ MakePasta(x)))

∀x (MakeCookies(x) ∧ MakeMuffins(x) → Baker(x))

∀x ((Baker(x) ∧ MakeScrambledEggs(x)) → MakeGoodBreakfast(x))

MakeCookies(luke) ∧ MakeScrambledEggs(luke) ∧ MakeMuffins(luke) ∧ ¬MakePasta(luke)


ETS develops assessments for K-12 statewide as well as entry to US tertiary and quaternary education institutions.

ETS develops various standardized tests primarily in the United States for K-12 and higher education.

ETS administers international tests including the TOEFL, TOEIC, GRE and subject tests in more than 180 countries.

Many of the assessments ETS develops are associated with entry to the US tertiary and quaternary education institutions.

ETS also develops K-12 statewide assessments used for accountability testing in many states.

∃x (Develops(ets, x) ∧ StandardizedTest(x) ∧ In(x, unitedstates) ∧ For(x, k-12andhighereducation))

∃x (Administers(ets, x) ∧ InternationalTest(x) ∧ (TOEFL(x) ∨ TOEIC(x) ∨ GRE(x) ∨ SubjectTests(x)))

∃x (Develops(ets, x) ∧ AssociatedWith(x, entrytouseducationinstitutions))

∃x (Develops(ets, x) ∧ StateWideAssesment(x) ∧ UsedFor(x, accountabilitytesting))


ETS doesn't administer tests internationally.


ETS administers international tests including the TOEFL, GRE and subject tests in China.


Robert can resist the hallmark delectable drinks and desserts that are famed in Italy.

All people who enjoy eating gelato ice cream would enjoy a vacation to Italy.

There are no people who can resist the hallmark delectable drinks and desserts that are famed in Italy.

People either enjoy eating gelato ice cream or love to travel and vacation often.

If people often take study abroad semesters to Europe, then they do not regret their college experiences.

If people love to travel and vacation often, then they often take study abroad semesters to Europe.

Robert either enjoys eating gelato ice cream and loves to travel and vacation often, or he neither enjoys eating gelato ice cream nor loves to travel and vacation often.

(Gelato(robert) ∧ Travel(robert)) ∨ (¬Gelato(robert) ∧ ¬Travel(robert))


If Robert either would both enjoy a vacation to Italy and regrets his college experiences or neither would enjoy a vacation to Italy nor regrets his college experiences, then Robert would either enjoy a vacation to Italy or, if not, then he can resist the hallmark delectable drinks and desserts that are famed in Italy.


If Robert is not both a person who can resist the hallmark delectable drinks and desserts that are famed in Italy and regrets his college experiences, then Robert either enjoys eating gelato ice cream or would enjoy a vacation to Italy.


To get a student visa, you must be full-time enrolled in an academic program.

Those who are full-time enrolled in an academic program can not work full-time.

Everyone who wants to study abroad needs to have a student visa.

If Tom does not want to study abroad, he is full-time enrolled in an educational program.

∀x (StudentVisa(x) → FullTimeAcademic(x))

∀x (FullTimeAcademic(x) → ¬WorkFullTime(x))


Sally's company utilizes the installment sales method.

The installment sales method is the approach to recognize revenue under the US GAAP.

In accrual accounting, revenues are recognized when they are realized.

In cash accounting, revenues are recognized when cash is received.

The US GAAP is the accounting standard developed and used by the US Securities and Exchange Commission.

Sally works for the US Securities and Exchange Commission.

∀x (UsesGAAP(x) → UsesInstallmentMethod(x))

∀x (UsesAccruralAccounting(x) → RecognizedWhen(revenues, realized))

∀x (UsesCashAccounting(x) → RecognizedWhen(revenues, cashrecieved))

DevelopedBy(usgaap, ussecuritiesandexchangecommission) ∧ UsesGAAP(ussecuritiesandexchangecommission)


The company Sally works for performs accrual accounting.


Sally does not work for a company that uses the GAAP.


All people who are respected by others are people who contribute to the country.

If a person is respected by others, then he/she contributes to the country.

All people available to have a visit without any fees are those respected by others.

All Customers who once served in the army are available to have a visit without any fees.

All people who once were sentenced for thief stayed in prison for some time.

All people who once stayed in prison for some time have a bad record in the local state.

James was either once sentenced for thief or stayed in prison for some time.

James is either with a bad record in the local state or respected by others.

∀x (Respected(x) → ContributeToCountry(x))

∀x (HaveVisitWithoutAnyFees(x) → Respected(x))

∀x (Army(x) → HaveVisitWithoutAnyFees(x))


James does not contribute to the country.


James contributes to the country, and he once served in the army.


James did not contribute to the country and did not serve in the army.


Water from the Croton River watershed flows to somewhere in New York.

The Croton River watershed is the drainage basin of the Croton River.

The Croton River is in southwestern New York.

Water from the Croton River watershed flows to the Bronx.

∃x (Water(x) ∧ From(x, crotonriverwatershed) ∧ FlowsTo(x, bronx))


The Croton River watershed is in the Bronx.


Water from the Croton River flows to the Bronx.


All nuclear-powered submarines are warships.

No nuclear-powered submarines are commercial vessels.

∀x (NuclearPoweredSubmarine(x) → Warship(x))

∀x (NuclearPoweredSubmarine(x) → ¬CommercialVessel(x))


The genre of Trouble at the Henhouse is rock.

If a album is written by a rock band, then the genre of the album is rock.

If a band writes a album winning an award, then this band wins this award.

Trouble at the Henhouse is an album by The Tragically Hip.

The Tragically Hip is a Canadian rock band.

The song "Butts Wigglin'" is in Trouble at the Henhouse.

Trouble at the Henhouse won the Album of the Year award.

A song in Trouble at the Henhouse appeared in a film.

∀x ∀y ∀z (AlbumByBand(x, y) ∧ RockBand(y, z) → Genre(x, rock))

∀x ∀y ∀z (AlbumByBand(x, y) ∧ AlbumAward(x, z) → RockBandAward(y, z))

∃x (SongInFilm(x) ∧ SongInAlbum(x, trouble_at_the_Henhouse))


A canada rock band didn't win the Album of the Year award.


Daniel once applied to Stanford University, but he couldn’t get in even though he has family members who are Stanford alumni.

Daniel is a software engineer and he works at Palantir Technologies.

Daniel studied bioengineering during his undergraduate at Rice University.

Daniel’s older sister works at Meta as a technical sourcer.

Daniel’s dad and older sister both graduated from Stanford University.

Daniel’s dad is a doctor practicing internal medicine at a veteran’s hospital in Minneapolis

SoftwareEngineer(daniel) ∧ WorksAt(daniel, palantirTechnologies)


Daniel studied bioengineering as his major at Rice University.


Daniel and his sister grew up in Minneapolis, Minnesota.


An American Airlines plane is either a Boeing or Airbus plane.

All commerical aircraft are produced by either Boeing or Airbus.

All American Airlines jets are commerical aircraft.

Airbus made more in revenue than Boeing last year.

∀x (CommercialAircraft(x) → ProducedBy(x, boeing) ⊕ ProducedBy(x, airbus))

∀x (AmericanAirlinesAircraft(x) → CommercialAircraft(x))


There exists a SpaceX commerical aircraft.


There does not exist a United Airlines plane produced by Boeing.


There is a commercial plane made by both Airbus and Boeing.


In December 1999, an earthquake struck Luzon.

People died in the December 1999 earthquake in Luzon.

∃x (Earthquake(x) ∧ StruckIn(x, december1999) ∧ Struck(x, luzon))

∃x (Earthquake(x) ∧ StruckIn(x, december1999) ∧ Struck(x, luzon) ∧ Killed(x))


No one has ever died of an earthquake that struck in the Philippines.


In 1999, there was at least one earthquake in the Philippines.


Matt reads the Wall Street Journal and other newspapers regularly to keep updated on financial metrics.

People either invest in the public stock market regularly or enjoy gambling regularly.

If people invest in the public stock market regularly, then they read the Wall Street Journal and other newspapers regularly to keep updated on financial metrics.

All people who enjoy gambling regularly spend a lot of money at casinos and other betting games.

People who spend a lot of money at casinos and other betting games visit the Las Vegas Strip regularly.

People who spend a lot of money at casinos and other betting games have a lot of disposable income to spend.

If Matt invests in the public stock market regularly, then Matt neither has a lot of disposable income to spend nor invests in the public stock market regularly.

Invests(matt) → ¬DisposableIncome(matt) ∧ ¬Invests(matt)


If Matt is either both a person who has a lot of disposable income to spend and invests in the public stock market regularly, or neither has a lot of disposable income to spend nor invests in the public stock market regularly, then Matt neither visits the Las Vegas Strip regularly nor reads the Wall Street Journal and other newspapers regularly to keep updated on the financial metrics.


If Matt is either a person who has a lot of disposable income to spend or reads the Wall Street Journal and other newspapers regularly, then Matt neither has a lot of disposable income to spend nor visits the Las Vegas Strip Regularly.


All students learning piano can strike the right notes.

All students who can strike the right note can get the rhythms right.

If a student can get the rhythms right, he will start working on coordination between the left and the right hands.

Some students who start working on coordination between the left and the right hands become good at it. The other students find it challenging.

If John can strike the right notes, get the rhythms right and is good at coordination between right and left hands, then he puts emotions into his playing.

John does not find coordination between the left and the right hands challenging.

∀x (Student(x) ∧ LearningPiano(x) → StrikeRightNotes(x))

∀x (Student(x) ∧ StrikeRightNotes(x) → GetRhythmRight(x))

∀x (Student(x) ∧ GetRhythmRight(x) → StartCoordination(x))

∀x (Student(x) ∧ StartCoordination(x) → GoodAtCoordination(x) ⊕ FindCoordinationChallenging(x))

StrikeRightNotes(john) ∧ GetRhythmRight(john) ∧ GoodAtCoordination(john) → PutEmotion(john)


John does not put emotions into his playing.


Barbara Ann Marshall did not receive medals.

Barbara Ann Marshall is a former swimmer and former world record-holder.

Barbara Ann Marshall participated in the 1972 Summer Olympics.

Barbara Ann Marshall's home country is the United States.

All people who compete in the 1972 Summer Olympics represent their home country.

Barbara Ann Marshall participated in the preliminary heat in the freestyle relay.

Barbara Ann Marshall did not participate in the event final of the 1972 Summer Olympics freestyle relay.

Only relay swimmers who participated in the event final received medals.

∀x ∃y (ParticipatedIn(x, summer1972olympics) ∧ HomeCountry(x, y) → Represented(x, y))

∀x ((RelaySwimmer(x) ∧ ¬ParticipatedIn(x, finalheatfreerelay)) ↔ ¬Recieved(x, medal)))


Barbara Ann Marshall represented the United States in the 1972 Summer Olympics.


It is possible to move to the green stage without ever reaching the yellow stage.

A game is played with three stages: red stage, yellow stage, and green stage.

All players must reach the yellow stage before they can reach the green stage.

The yellow stage comes after the red stage.

All players must proceed one stage at a time.

∃x (Player(x))
∀x (Player(x) → StartRed(x))
∀x (Player(x) → YellowToGreen(x))
∀x (Player(x) → RedToYellow(x))
∀x (Player(x) → ¬RedToGreen(x))


It is possible to reach the yellow stage without ever reaching the green stage.


It is possible to complete the game without ever reaching the green stage.


People either value physical touch as an especially important love language or value words of affirmation as an especially important love language.

If a person values physical touch as an especially important love language, then they are good with pets.

No people that are good with pets are scared of animals.

People are either scared of animals or love animals.

Adam is either a person who values physical touch as an especially important love language or a person who loves animals.

∀x (GoodWithPets(x) → ¬ScaredOfAnimals(x))

∀x (ScaredOfAnimals(x) ∨ LoveAnimals(x))


Adam values words of affirmation as an especially important love language.


Adam values physical touch as an especially important love language and values words of affirmation as an especially important love language.


Adam either values physical touch as an especially important love language or values words of affirmation as an especially important love language.


If Adam values physical touch as an especially important love language or is good with pets, then Adam values words of affirmation as an especially important love language.


If something is an iguana, then it is a reptile.

∀x (Bird(x) → Winged(x))
∀x (Winged(x) → ¬Reptile(x))
∃x (Fly(x) ∧ Bird(x))
∀x (Iguana(x) → Reptile(x))
¬Iguana(john) ⊕ Bird(john)


John is not an iguana and an animal that can fly.


John is an animal that can fly and a bird.


EndGame was filmed outside of Washington.

Movie(endGame) ∧ Released(endGame, year2006)


EndGame was not directed by someone from Hong Kong.


All of Andy Chang's movies are filmed outside of Washington.


If a real number equals another real number adding one, the first number is larger.

If the number x is larger than number y, then y is not larger than x.

If a number is positive, then the double of it is also positive.

RealNum(six) ∧ RealNum(seven) ∧ RealNum(eight)

∀x ∀y (RealNum(x) ∧ RealNum(y) ∧ EqualAddOne(x, y) → Larger(x, y))

∀x ∀y ((Positive(x) ∧ EqualDouble(y, x)) → Positive(y))


Some poker players never tell the truth.

A dog never tells the truth.
Some poker players are dogs.

∀x (Dog(x) → NeverTellsTruth(x))
∃x (PokerPlayer(x) ∧ Dog(x))


Jessee is either both an Indian and a human, or neither an Indian nor a human.

( Indian(jesse) ∧ Human(jesse)) ⊕ (¬ Indian(jesse) ∧ ¬ Human(jesse))


If Jesse is either an Indian or a Spanish, then Jesse is either both British and European, or neither British nor European.


Some good teachers are not well-informed people.

No people who never admit a mistake are good teachers.

Some well-informed people are people who never admit a mistake.

∀x (NeverAdmitMistakes(x) → ¬GoodTeacher(x))

∃x (WellInformed(x) ∧ NeverAdmitMistakes(x))


Philatelic literature is divided into the following categories: Stamp catalogues, Periodicals, Auction catalogues, Books, Bibliographies, and Background Material

Mort is not a periodical, auction catalogue, bibliography, or background material.

Mort is a piece of Philatelic literature.

∀x (PhilatelicLit(x) → (Stamp(x) ∨ Periodical(x) ∨ Auction(x) ∨ Book(x) ∨ Bibliography(x) ∨ Background(x)))

¬(Periodical(mort) ∨ Auction(mort) ∨ Bibliography(mort) ∨ Background(mort))


Eragon is a piece of Philatelic literature.


Adventures of Rusty is a drama film and children's film.

Columbia Pictures produced Adventures of Rusty


Columbia pictures produces adventure films.


The paramount leader of the PRC was also the vice premier.

Deng Xiaoping served as the paramount leader of the People's Republic of China (PRC).

Deng Xiaoping was praised for his reaffirmation of the reform program in his Southern Tour of 1992 as well as the reversion of Hong Kong to Chinese control in 1997 and the return of Macau in 1999.

As the party's Secretary-General under Mao and Vice Premier in he 1950s, Deng Xiaoping presided over the Anti-Rightist Campaign launched by Mao.

Deng Xiaoping became instrumental in China's economic reconstruction following the disastrous Great Leap Forward (1958–1960).

After Mao Zedong's death, Deng Xiaoping gradually rose to supreme power.

PraisedFor(dengxiaoping, reaffirmationofreformprogram) ∧ PraisedFor(dengxiaoping, reversionofhongkong) ∧ PraisedFor(dengxiaoping, returnofmacau)

PartysSecretaryGeneral(dengxiaoping) ∧ Under(dengxiaoping, mao) ∧ VicePremier(dengxiaoping) ∧ PresidedOver(dengxiaoping, antirightistcampaign) ∧ LaunchedBy(antirightistcampaign, mao)

InstrumentalIn(dengxiaoping, chinaseconomicreconstruction) ∧ Following(chinaseconomicreconstruction, greatleapforward) ∧ Disastrous(greatleapforward)


Deng Xiaoping presided over something launched by someone he was under.


The person instrumental in china's economic reconstruction gradually rose to supreme power.


All imaginative processes are produced in human brains.

All science-fiction is from an imaginative process.

Dune is a science-fiction or proven to be false.

∀x (ImaginativeProcess(x) → ProducedInHumanBrains(x))

∀x (Science-fiction(x) → ImaginativeProcess(x))


Dune is produced in human brains and is an imaginative process.


Dune is either produced in human brains or an imaginative process.


Dune is produced in human brains and is science fiction.


Dune is either produced in human brains or science-fiction.


If Dune is produced in human brains and is an imaginative process, then Dune is not produced in human brains and science-fiction.


If Dune is either a fact and produced in human brains, or neither a fact nor produced in human brains, then Dune is produced in human brains and science-fiction.


If Dune is science-fiction, then Dune is not produced in human brains and science-fiction.


If Dune is not produced in human brains and science-fiction, then Dune is neither an imaginative process nor proved to be false.


If Dune is not an imaginative process and science-fiction, then Dune is neither produced in human brains nor an imaginative process.


An American superhero comes from either DC universe or Marvel universe.

Captain America does not come from DC universe.

If a superhero is American, he speaks English.

∀x (Superhero(x) ∧ American(x) → (ComeFrom(x, dc universe) ⊕ ComeFrom(x, marvel universe)))

∀x (Superhero(x) ∧ American(x) → Speak(x, english))

∀x (Superhero(x) → (Speak(x, english) ∨ Speak(x, spanish)))


Captain America comes from Marvel universe.


Robert Zimmer was born in Germany.
Robert Zimmer is an essayist.
Robert Zimmer was born in 1953.
Every essayist is a writer.
Every person born in Germany is German.

BornInGermany(robertZimmer)
IsEssayist(robertZimmer)
BornIn(robertZimmer, year1953)
∀x (IsEssayist(x) → IsWriter(x))
∀x (BornInGermany(x) → IsGerman(x))


If John repays his loans on time, he will be approved for a mortgage.

All people who repay their loans on time have a high credit score.

Some people with high credit scores and high salaries are approved for mortgages.

∃x ((HighCreditScore(x) ∧ HighSalary(x)) → Mortgage(x))


All students are members of the university.

If John is not a PhD student, then he is not a member of the university.

If John has a high IQ, then he is a PhD student or a graduate student.

HighIQ(john) → PhDStudent(john) ⊕ GraduateStudent(john)


If John goes to Europe, he will see the Eiffel Tower.

Belgium, France and Germany are European countries.

The Eiffel Tower is one of the main tourist attractions located in Paris.

Some people who live in Belgium speak French.

If John goes to Europe, he will see some tourist attractions.

EuropeanCountry(belgium) ∨ EuropeanCountry(france) ∨ EuropeanCountry(germany)

TouristAttraction(eiffelTower) ∧ LocatedIn(eiffelTower, paris)

∃x (LiveIn(x, belgium) → Speak(x, french))

∃x (GoTo(john, europe) → (See(john, x) ∧ TouristAttraction(x)))


The Eiffel Tower is located in the capital of France.


If a car is a Ferrari, then it is a sports car.

If Prius is neither a sports car nor a loud car, then Prius is a Maranello-made car or a loud car.

∀x (¬SportsCar(prius) ∨ ¬LoudCar(prius) → MadeInMaranello(prius) ∨ LoudCar(prius))


If Prius is a Ferrari or a loud car, then Prius is an electric car.


If something is a plant, then it is not a cute animal.

If something is grown in a garden, then it is a flower.

∀x (Plant(x) → ¬CuteAnimal(x))
∀x (Flower(x) → Plant(x))
∀x (Kitten(x) → CuteAnimal(x))
∀x (GrownInGarden(x) → Flower(x))
Kitten(piper) ∨ CuteAnimal(piper)


Judd Bankert competed in the 1992 Winter Olympics.

Guam has participated in the Winter Olympics.

In 1988, the Winter Olympics were held in Calgary.

Guam sent an athlete to the Calgary Winter Olympics.

If Guan sent an athlete to the Calgary Winter Olympics, then it participated in the Calgary Winter Olympics.

Judd Bankert is the only athlete from Guam who has ever competed in the Winter Olympics.

Year(y1988) → BeHeld(winterolympics, calgary)

BeHeld(winterolympics, calgary) → SendAthletes(guam)

SendAthletes(guam) → ParticipatedIn(guam, winterolympics)

BeFrom(bankert, guam) ∧ ParticipatedIn(bankert, winterolympics)


Guam has participated in the Summer Olympics at least once.


The son of a general practitioner was a word-setter of My Word!.

Michael O'Donnell is a British physician, journalist, author and broadcaster.

One of the word-setters of My Word! was Michael O'Donnell.

The magazine World Medicine was edited by Michael O'Donnell.

Michael O'Donnell was born in Yorkshire as the son of a general practitioner.

British(michael) ∧ Physician(michael) ∧ Journalist(michael) ∧ Author(michael) ∧ Broadcaster(michael)

Magazine(worldmedicine) ∧ EditedBy(worldmedicine, michael)

∃x (BornIn(michael, yorkshire) ∧ Son(michael, x) ∧ GeneralPractitioner(x))


There are no journalists that were born in Yorkshire.


There is a son of a general practitioner that is not an author.


No homework is fun.
Some reading is homework.

∀x (Homework(x) → ¬IsFun(x))
∃x (IsReading(x) ∧ Homework(x))


If something is justified, it is lawful.

∀x ((Violence(x) ∧ Good(x)) → Justified(x))


Manny regularly rides horses for pleasure and sport.

All people who have a horse ranch regularly ride horses for pleasure and sport.

All people who have a lot of disposable income have a horse ranch.

If people compete in horse dressage shows, then they have a lot of disposable income.

If people compete in horse dressage shows, then they have invested in high-quality equestrian gear and equipment.

If people regularly ride horses for pleasure and sport, then they do not live in cramped residential buildings.

Manny either has a horse ranch and lives in cramped residential buildings, or he neither has a horse ranch nor lives in cramped residential buildings.

(Ranch(manny) ∧ Cramped(manny)) ⊕ (¬Ranch(manny) ∧ ¬Cramped(manny))


Manny competes in horse dressage shows and has invested in high-quality equestrian equipment and gear.


If Manny either has a horse ranch or competes in horse dressage shows, then Manny has not invested in high-quality equestrian equipment and gear.


Cannons can be deployed on battery towers.

A roundel is a rounded artillery fortification.

A roundel is not higher than adjacent walls.

Cannons can be deployed on artillery fortifications.

Roundels are the oldest artillery fortifications.

Battery towers are an artillery fortification.

∀x (Roundel(x) → Rounded(x) ∧ ArtilleryFortification(x))

∀x ∀y (Roundel(x) ∧ AdjacentWall(y) → ¬Higher(x, y))

∀x (ArtilleryFortification(x) → DeployCannons(x))

∀x ∀y (Roundel(x) ∧ ArtilleryFortification(x) ∧ ArtilleryFortification(y) → Older(x, y))

∀x (BatteryTower(x) → ArtilleryFortification(x))


Battery towers are higher than adjacent walls.


All tissues are soft.
Some papers are tissues.

∀x (Tissue(x) → Soft(x))
∃x (Paper(x) ∧ Tissue(x))


Volunteers who participate in natural disaster response receive intangible benefits for their work.

All volunteers receive intangible benefits for their work.

Volunteers work regularly or on an as-needed basis.

Volunteers work in groups or individually.

Environmental volunteers contribute toward environmental management or conservation.

Participating in natural disaster response is an example of volunteers working in groups on an as-needed basis.

∀x (Volunteer(x) → GetIntangibleBenefits(x))

∀x (Volunteer(x) → WorkRegularly(x) ∨ WorkAsNeeded(x))

∀x (Volunteer(x) → (WorkInGroup(x) ∨ WorkIndividually(x)))

∀x (Volunteer(x) ∧ Environmental(x) → (ContributeTo(x, environmentalmanagement) ∨ ContributeTo(x, environmentalconservation)))

∃x (Volunteer(x) ∧ ContributeTo(x, naturaldisasterresponse) → WorkInGroup(x) ∧ WorkAsNeeded(x))


Environmental volunteers work in groups.


Mike is an old person living in a stable home.

All people who are very consistent and enjoy sticking to their regular routines do not like surprises.

If people wear flannel shirts every day, then they are very consistent and enjoy sticking to their regular routines.

If people do not like shopping for clothes and other materialistic goods, then they wear flannel shirts every day.

All old people living in stable homes do not like surprises.

If people have very high energy and are impulsive, then they like surprises.

If Mike is not a person who wears flannel shirts every day and has very high energy and is impulsive, then Mike either is very consistent and enjoys sticking to his regular routines or does not like surprises.

¬(NoSurprises(mike) ∧ Impulsive(mike)) → Consistent(mike) ⊕ NoSurprises(mike)


If Mike wears flannel shirts every day or does not like shopping for clothes and other materialistic goods, then Mike is neither an old person living in a stable home nor does not like shopping for clothes and other materialistic goods.


If Mike is not an old person living in a stable home and does not like shopping for clothes and other materialistic goods, then Mike does not like shopping for clothes and other materialistic goods.


Among the cars he owns, Adam's favorite car is European.

∀x ((Owns(adam, x) ∧ Favorite(adam, x)) → European(x))

∀x ((Owns(adam, x) ∧ Favorite(adam, x)) → Broke(adam, x))


No buildings in New Haven are higher than 400 meters.

All buildings managed by Yale Housing are in New Haven.

All buildings in Manhattan are higher than 400 meters.

All buildings owned by Bloomberg are in Manhattan.

All buildings with the Bloomberg logo are buildings owned by Bloomberg.

Tower A is neither in New Haven nor in Manhattan.

Tower B is a building with the Bloomberg logo and in Manhattan.


Tower A is a building with the Bloomberg logo or managed by Yale Housing.


Tower A is neither a building with the Bloomberg logo nor managed by Yale Housing.


If something is a carp, then it is a fish.

If Bubbles is either an osprey or a goldfish, then Bubbles is not a fish.

Osprey(bubbles) ⊕ Carp(bubbles) → ¬Fish(bubbles)


Mr. and Mrs. Smith make a travel plan, they want to go to a city in California or Florida, and where neither of them has ever been.

Cities in California that they are interested in are San Francisco, Los Angeles, and San Diego.

Cities in Florida that they are interested in are Orlando and Miami.

Mr. Smith has been to two cities in California.

Mrs. Smith has been to one city in Florida.

∀x (WantToGo(x) → (California(x) ∨ Florida(x)) ∧ (NeverGo(x)))

∀x (((SanFrancisco(x) ∨ LosAngeles(x) ∨ SanDiego(x)) ∧ California(x)) → WantToGo(x))

∀x ((Orlando(x) ∨ Miami(x)) ∧ Florida(x)) → WantToGo(x))


They have at leat one candidate city in Florida to visit.


They have at least two candidate cities in California to visit.


Everything is either big or small.
All big things are heavy.
All small things are light.
All heavy things are still.
All light things are unstable.
All unstable things are changing.
All unstable things are kinetic.
A bird is not both heavy and still.

∀x (Big(x) ⊕ Small(x))
∀x (Big(x) → Heavy(x))
∀x (Small(x) → Light(x))
∀x (Heavy(x) → Still(x))
∀x (Light(x) → Unstable(x))
∀x (Unstable(x) → Changing(x))
∀x (Unstable(x) → Kinetic(x))
¬(Heavy(bird) ∧ Still(bird))


If a bird is small or still, then the bird is either kinetic or changing.


DI Ray is a police procedural television series.

DI Ray was created and written by Maya Sondhi.

Maya Sondhi and Jed Mercurio are both British.

Create(maya, diRay) ∧ Write(maya, diRay)


If Mike is not both a human and a sheep, then Mike is either a man or a human.

(¬Human(mike) ∨ ¬Sheep(mike)) → Man(mike) ⊕ Human(mike)


If Mike is a gentleman or a lawyer, then Mike is neither a woman nor a lawyer.


If Mike is not both a woman and a lawyer, then Mike is a lawyer.


No soccer players are professional basketball players.

All NBA players are professional basketball players.

¬(∃x (SoccerPlayer(x) ∧ ProfessionalBasketballPlayer(x)))

∀x (NBAPlayer(x) → ProfessionalBasketballPlayer(x))


Stephen Curry is not a centerback and a defender.


If Stephen Curry is not a centerback and a defender, then Stephen Curry is neither a soccer player nor a professional basketball player.


If a person doesn't have enough money to buy a product, then that person can't buy it.

4k monitors are more expensive than 1080 monitors and 2k monitors.

John doesn't have enough money to buy a 2k monitor.

∀x ∀y (Person(x) ∧ Product(y) ∧ ¬HaveEnoughMoneyFor(x, y) → ¬Buy(x, y))

∀x ∀y ∀z (Monitor(x) ∧ Monitor(y) ∧ Monitor(z) ∧ FourK(x) ∧ OneOEightO(y) ∧ TwoK(z) → MoreExpensive(x, y) ∧ MoreExpensive(x, z))

∀x (Monitor(x) ∧ TwoK(x) → ¬HaveEnoughMoneyFor(john, x))


All important scientific achievements are U.S. inventions.

All artificial satellites are important scientific achievements.

Some artificial satellites are not U.S. inventions.

∀x (ArtificialSatellite(x) → ImportantScientificAchievement(x))

∃x (ArtificialSatellite(x) ∧ ¬USInvention(x))


Some cats are not pets.
All cats are mammals.

∃x (Cat(x) ∧ ¬Pet(x))
∀x (Cat(x) → Mammal(x))


Sam is addicted to coffee and other caffeinated drinks.

If people visit a coffee shop at least three times a week, then they are addicted to coffee or other caffeinated drinks.

People either visit a coffee shop at least three times a week or order takeout at least once a day.

If people make a lot of their own food at home using recipes and online guides, then they order takeout at least once a day.

If people own at least one coffeemaker and one blender in their home, then they do not order takeout at least once a day.

All people who lead very busy lives that include 12-hour work hours make a lot of their own food at home using recipes and online guides.

Sam is either both addicted to coffee or other caffeinated drinks or leads very busy lives that include 12-hour work hours, or she is neither addicted to coffee and other caffeinated drinks nor leads very busy lives that include 12-hour work hours

(CaffeineAddict(sam) ∧ Busy(sam)) ⊕ (¬CaffeineAddict(sam) ∧ ¬Busy(sam))


Sam owns at least one coffeemaker and one blender in her home.


Sam either owns at least one coffeemaker and one blender in her home or orders takeout at least once a day.


No professional basketball players are soccer players.

Roger Federer is not an NBA player or a defender.


Some teachers working at a pool are not nice.

All teachers working at pools are pool managers.

If someone is a lifeguard, then they work at a pool.

∀x (TeacherWorkingAtPool(x) → PoolManager(x))


Mary is not nice and is a teacher working at a pool.


Mary is nice and is a teacher working at a pool.


There exist art pieces that do not require practice.

Everything that requires talent requires practice.

∀x (RequiresTalent(x) → RequiresPractice(x))


Bernarda Bryson Shahn was born in Greece.

Bernarda Bryson Shahn was a painter and lithographer.

Bernarda Bryson Shahn was born in Athens, Ohio.

Bernarda Bryson Shahn was married to Ben Shahn.

People born in Athens, Ohio are Americans.

∀x (BornIn(x, athensOhio) → American(x))


Bernarda Bryson Shahn had been divorced once.


If people upgrade to the newest iPhone model every year, then they are not saving money for a down payment on a new house.

If people enjoy reading about tech specs and keeping up to date on the latest technology, then they upgrade to the newest iPhone model every year.

People either are saving money for a down payment on a new house or they live in apartments in big metropolitan cities.

If people live with at least one roommate then they do not own at least one pet.

All people who own at least one pet live with at least one roommate.

If Emma does not both own at least one pet and live in apartments in big metropolitan cities, then Emma either owns at least one pet and lives in an apartment in big metropolitan cities, or she neither owns a pet nor lives in an apartment in big metropolitan cities.

¬(Pet(emma) ∧ Apartment(emma)) → ((Pet(emma) ∧ Apartment(emma)) ∨ (¬Pet(emma) ∧ ¬Apartment(emma)))


Emma enjoys reading about tech specs and keeping up to date on the latest technology.


If you are on the payroll, then you are being paid by the school.

If someone has a job at a school, then they are on the payroll.

All faculty members have a job at a school.

One can either be a faculty member or a teacher.

If Nancy is a teacher, then they are on the payroll.

If Nancy is not a teacher, then they are not paid by the school.

∀x (OnPayroll(x) → PaidBySchool(x))
∀x (JobAtSchool(x) → OnPayroll(x))
∀x (FacultyMember(x) → JobAtSchool(x))
∀x (FacultyMember(x) ∨ Teacher(x))
∀x (Teacher(x) → HasStudents(x))
Teacher(nancy) → OnPayroll(nancy)
¬Teacher(nancy) → ¬OnPayroll(nancy)


Nancy is paid by the school and has students.


Nancy is not paid by the school and has students.


If Jane saves enough money for the summer, she will see a kangaroo.

If Jane saves enough money for the summer, she will fly to Germany.

If Jane flies to Germany, she will go to the Berlin Zoo.

If someone goes to the Berlin Zoo, they will see some of the animals that live in Germany.

EnoughMoney(jane) → FlyTo(jane, germany)

FlyTo(jane, germany) → GoTo(jane, berlinzoo)

∀x ∃y (GoTo(x, berlinzoo) ∧ Animal(y) → MaySee(y, x, berlinzoo))


If a class has prerequisites the student must take the prerequisites to take the class.

If a class has no prerequisites, then the student can take the class

CPSC 201 and CPSC 223 are prerequisites for CPSC 323.

Intro Microeconomics is the only prerequisite for Intermediate Microeconomics.

∀x ∀y ((Prereq(x, y) ∧ Taken(x)) ↔ CanTake(y))

Prereq(cpsc201, cpsc323) ∧ Prereq(cpsc223, cpsc323)

(Prereq(intromicro, intermediatemicro) ∧ Taken(intromicro)) → CanTake(intermediatemicro)


If a student took CPSC 201 but did not take CPSC 223, they can take CPSC 323.


Intermediate Microeconomics has one prerequisite.


The Harry Potter series of books is a heptalogy.

A heptalogy, is a compound literary or narrative work that is made up of seven distinct works.

The Harry Potter series consists of 7 distinct works.

The Chronicles of Narnia consists of 7 distinct works.

∀x (SevenDistinctWorks(x) → Heptalogy(x))


The Chronicles of Narnia series of books is not a heptalogy.


Clyde attends Renaissance fairs regularly.

All people who attend Renaissance fairs regularly enjoy dressing up in old-fashioned and historical period clothing.

If people are fascinated by the history of the Renaissance and other past eras, then they attend Renaissance fairs regularly.

People are either fascinated by the history of the Renaissance and other past eras, or are not nostalgic academics who enjoy learning.

If people are focused on the future and industry professions, then they are not nostalgic academics who enjoy learning.

If people are historical professors who are passionate about their job and subject, then they are nostalgic academics who enjoy learning.

If Clyde is not focused on the future and industry professions, then he is neither focused on the future and industry professions nor enjoys dressing up in old-fashioned and historical period clothing.

∀x (HistoryRenaissance(x) → RenaissanceFair(x))

∀x (HistoryRenaissance(x) ∨ NotAcademics(x))

¬Industry(clyde) → ¬(Industry(clyde) ∨ DressingUp(clyde))


Clyde is a history professor who is passionate about his job and subject.


Clyde is a history professor who is passionate about his job and subject, or is not a nostalgic academic who enjoys learning.


No sports cars are automobiles designed for family use.

No sports cars are vehicles intended to be driven at moderate speeds.

All automobiles designed for family use are vehicles intended to be driven at moderate speeds.

∀x (SportsCar(x) → ¬IntendedToBeDrivenAtModerateSpeeds(x))

∀x (ForFamilyUse(x) → IntendedToBeDrivenAtModerateSpeeds(x))


Kat is a person who comes to work every day with a positive attitude.

If people work well in teams in their workplace, then they get along with all their colleagues at their work.

If people come to work every day with a positive attitude, then they work well in teams in their workplace.

People either come into work every day with a positive attitude or are always tired every morning.

If people get many promotions from their boss at work, then they receive negative feedback from teams at work.

Kat is either both a person who works well in teams in their workplace and is always tired every morning, or she neither works well in teams in their workplace nor is always tired every morning.

∀x (PositiveAttitude(x) ⊕ Tired(x)) ∧ (∀x (Tired(x) → BossPromotions(x)))

∀x (BossPromotions(x) → ¬NegativeFeedback(x))

(WorkTeams(kat) ∧ Tired(kat)) ∨ ¬WorkTeams(kat) ∧ ¬Tired(kat))


Kat gets along with her colleagues at her work and receives negative feedback from teams at her work.


Kat either gets along with her colleagues at her work or receives negative feedback from teams at her work.


Drishti is open-source.
Open-source software is free to modify.

OpenSource(drishti)
∀x (OpenSource(x) → ModifyFree(x))


There are five grades including A+, A, B+, B, and C in English.

If a student gets A+ in English, then his score is greater than 95.

If a student gets A in English, then his score is in the range of 90-95.

Wang's English score is better than Zhang's.

Grade(a+) ∨ Grade(a) ∨ Grade(b+) ∨ Grade(b) ∨ Grade(c)


At all times, Olivia prefers cool temperature.

Olivia doesn't prefer warm temperature during the day.

When Olivia sleeps, she prefers cool temperature.

The time is either the day or the night.

Olivia either prefers warm temperature or prefers cool temperature.

∀x (SleepingDuring(olivia, x) → PrefersCoolAt(olivia, x))

∀x (SleepingDuring(olivia, x) → Night(x))

∀x (WorkingDuring(olivia, x) ∨ SleepingDuring(olivia, x))

∀x (PrefersWarmAt(olivia, x) ∨ PrefersCoolAt(olivia, x))


Taylor Swift delivers a commencement speech in Manhattan.

Taylor Swift gives a commencement speech in New York University in 2022.

Both Columbia University and New York University are located in Manhattan.

Taylor Swift has received three Grammy Album of the Year Awards.

Columbia University is one of the Ivy League schools.


The commencement speaker of NYU does not have any album.


James is a customer who does not choose any plans.

Customers either choose Plan A or Plan B.

All who choose Plan B are rewarded with a $30 gift card.

There are no customers who do not choose any plans.

No customers rewarded a $30 gift card are older than 80.

Customers are either older than 80 or are currently studying at school.

James is not a customer who is currently studying at school.

∀x (PlanA(x) ∨ PlanB(x))
∀x (PlanB(x) → Award(x))
∀x (¬NoPlan(x))
∀x (Award(x) → ¬OlderThan80(x))
∀x (OlderThan80(x) ∨ StudyAtSchool(x))
¬StudyAtSchool(james)


James is a customer who chooses Plan A or does not choose any plans.


Suppose James is a customer who chooses Plan A or does not choose any plans, then he is either rewarded a $30 gift card or chooses Plan B.


Detroit City has been in multiple races.

If a horse falls during a race, then it dies.

A horse is a racehorse if it is in a race.

∀x (Horse(x) ∧ Racing(x) ∧ Falls(x) → Dead(x))

∀x (Horse(x) ∧ Racing(x) → Racehorse(x))


Frederick Monhoff was an architect, artist, and illustrator.

Architect(monhoff) ∧ Artist(monhoff) ∧ Illustrator(monhoff)

∀x (Artist(x) → GoodAt(x, painting) ∨ GoodAt(x, music))


There is no illustrator who speaks English.


Miroslav Fiedler is honored by the second smallest eigenvalue of the graph Laplacian.

Miroslav Fiedler was a Czech mathematician.

Miroslav Fiedler is known for his contributions to linear algebra and graph theory.

Miroslav Fiedler is honored by the Fiedler eigenvalue.

Fiedler eigenvalue is the second smallest eigenvalue of the graph Laplacian.


Miroslav Fiedler was a French mathematician.


A Czech mathematician is known for his contributions to linear algebra and graph theory.


A laptop is a computer.
You can play games on a computer.
A phone is not a computer.

∀x (Laptop(x) → Computer(x))
∀x (Computer(x) → CanPlayGames(x))
∀x (Phone(x) → ¬Computer(x))


Walter Folger Brown graduated with a Bachelors of Arts.

Walter Folger Brown was an American politician and lawyer, and served as the postmaster general.

Walter Folger Brown graduated from Harvard University with a Bachelors of Arts.

While they were both in Toledo, Walter Folger Brown's father practiced law with Walter Folger Brown.

Katherin Hafer married Walter Folger Brown.

AmericanPolitician(walterbrown) ∧ Lawyer(walterbrown) ∧ ServedAs(walterbrown, postamastergeneral)

Graduated(walterbrown, harvard) ∧ GraduatedWith(walterbrown, bachelorsofart)

In(walterbrown, toledo) ∧ In(walterbrownfather, toledo) ∧ PracticedLawTogether(walterbrownfather, walterbrown)


Walter Folger Brown's father was in Toledo.


All products shipped from China are made in China.

All products sold in JD are shipped from China.

All products commonly used in China are sold in JD.

All products favored by young people are commonly used in China.

MacBook is not made in China and is not commonly used in China.

∀x (FavoredByYoungPeople(x) → CommonlyUsedChina(x))


The MacBook is favored by young people and commonly used in China.


The MacBook is either favored by young people or commonly used in China.


If the MacBook is favored by young people and commonly used in China, then it is neither favored by young people nor made in China.


Oxford Circus is a road junction connecting Oxford Street and Regent Street.

John Nash designed the construction on Regent Street.

Oxford Circus is the entrance to Oxford Circus tube station which is a part of the Central line in 1900.

∃x (RegentStreet(x) ∧ Design(johnNash, x))


Oxford Circus is designed by a British architect.


John Nash designed the Central line in 1900.


If something barks, then it is not alive.

∀x (Cat(x) ⊕ Dog(x))
∀x (Dog(x) → Bark(x))
∀x (¬Ghost(x))
∀x (Bark(x) → ¬Alive(x))
∀x (Alive(x) ⊕ Dead(x))
¬Dead(jojo)


If Jojo is a cat or a ghost, then Jojo either barks or is a dog.


All animals that are tigers are cats.
No cats are dogs.
All Bengal tigers are tigers.
Everything that is a husky is a dog.
Fido is either a Bengal tiger or a cat.

∀x (Tiger(x) → Cat(x))
∀x (Cat(x) → ¬Dog(x))
∀x (BengalTiger(x) → Tiger(x))
∀x (Husky(x) → Dog(x))
BengalTiger(fido) ∨ Cat(fido)


The 2028 Summer Olympics will take place in the US.

If a city hold a Summer Olympics, and the city is a US city, then the Summer Olympics will be in the US.

If a city is in a state which is in US, the city is a US city.

If a city in a state, and a Summer Olympics is in this city, then the Summer Olympics is in this state.

The 2028 Summer Olympics is scheduled to take place in Los Angeles(LA).

Boxing, modern pentathlon, and weightlifting will be removed from The 2028 Summer Olympics.

Atlanta in the United States hold the 1996 Summer Olympics.

∀x ∀y (SummerOlympicsCity(x, y) ∧ CityInCountry(y, us) → SummerOlympicsCountry(x, us))

∀x ∀y (CityInState(x, y) ∧ StateInCountry(y, us) → CityInCountry(x, us))

∀x ∀y ∀z (CityInState(x, y) ∧ SummerOlympicsCity(z, x) → SummerOlympicsState(z, y))

¬InSummerOlympics(y2028, boxing) ∧ ¬InSummerOlympics(y2028, modern_pentathlon) ∧ ¬InSummerOlympics(y2028, weightlifting)


The 1996 Summer Olympics is not in Georgia.


Skateboarding will appear at The 2028 Summer Olympics.


The taiga vole is a large vole found in northwestern North America.

The taiga vole lives in the boreal taiga zone.

The boreal taiga zone in North America is a cold place to live in.

Taiga vole is typically much larger than most other North American voles, especially those from the genus Microtus.

Vole(taigaVole) ∧ Find(taigaVole, northAmerica)

∀x (Find(x, northAmerica) ∧ Live(x, borealTaigaZone) → LiveInColdPlace(x))


Either breast cancer or non-breast cancer.

All non-breast cancers are a type of cancer.

If adenocarcinoma is a type of cancer or without a tumor, then adenocarcinoma is in women or without a tumor.

∀x (BreastCancer (x) ∨ Non-BreastCancer(x))

∀x (ATypeOfCancer(x) → ¬WithoutTumor (x))

∀x (Non-BreastCancer(x) → ATypeOfCancer(x))

ATypeOfCancer(adenocarcinoma) ∨ WithoutTumor(adenocarcinoma) → women(adenocarcinoma) ∨ WithoutTumor(adenocarcinoma)


If adenocarcinoma is in women or without a tumor, then adenocarcinoma is without a tumor and a non-breast cancer.


Some monitors equipped in the lab are produced by the company named AOC.

All monitors equipped in the lab are cheaper than their original prices.

If the monitor is cheaper than its original prices, then its resolution is 1080p.

If a monitor is with a resolution of 1080p, then it does not support the type-c port.

∃x (Lab(x) ∧ AOC(x))
∀x (Lab(x) → Cheaper(x))
∀x (Cheaper(x) → A1080p(x))
∀x (A1080p(x) → ¬TypeC(x))
Lab(lg-34)


LG34 machine does not support the type-c port.


Avocados are a kind of fruit sold in New York.

All fruits sold in Boston are shipped from Columbia.

Some fruits sold in New Haven are shipped from Mexico.

No fruits shipped from Columbia are fruits sold in New York.

Avocadoe are a kind of fruit sold in New York or New York.

Avocadoe are either shipped from Columbia and sold in New Haven, or neither shipped from Columbia nor sold in New Haven.

∀x (SoldBoston(x) → ShippedFromColumbia(x))

∃x (SoldNewHaven(x) ∧ ShippedFromMexico(x))

∀x (ShippedFromColumbia(x) → ¬SoldNewYork(x))


Avocados are either sold in New York or sold in New Haven.


Avocados are either sold in New Haven or sold in Boston


If avocados are not sold in New York and not shipped from Columbia, then they are neither sold in New York nor New Haven.


Some monitors equipped in the library are produced by AOC.

All monitors equipped in the library are cheaper than 800 dollars.

All monitors cheaper than 800 dollars are with a resolution of 1080p.

If a monitor has a resolution of 1080p, then it does not support the type-c port.

∃x (Library(x) ∧ AOC(x))
∀x (Library(x) → Cheap(x))
∀x (Cheap(x) → A1080p(x))
∀x (A1080p(x) → ¬TypeC(x))
TypeC(a-2017)


A-2017 is produced by AOC and equipped in the library.


If A-2017 is not with a resolution of 1080p or produced by AOC, then it is not equipped in the library.


Some soccer team holds the Lithuanian Supercup.

Sūduva Marijampolė holds the Lithuanian Supercup.


Ainderby Quernhow is a village and civil parish in the Hambleton District.

Hambleton District is in North Yorkshire.

∀x (AinderbyQuernhow(x) → Village(x) ∧ CivilParish(x) ∧ Hambleton(x))


Douglas Adams is an author who created the book collection called The Salmon of Doubt.

The Salmon of Doubt is about life experiences and technology.

Some books that contain innovative ideas are about technology.

∀x (Writer(x) → CreateInnovativeIdea(x))

∃x (ContainInnovativeIdea(x) ∧ AboutTechnology(x))


The Salmon of Doubt has no innovative Ideas.


No disposable products can help slow down global warming.

All eco-friendly brands can help slow down global warming.

All sustainable fashion brands are eco-friendly brands.

All fast fashion products are disposable products.

If Reformation is not helping slow down global warming, then Reformation is an eco-friendly brand or a sustainable fashion brand.

∀x (DisposableProducts(x) → ¬HelpSlowDownGlobalWarming(x))

∀x (Eco-friendlyBrand(x) → HelpSlowDownGlobalWarming(x))

∀x (SustainableFashionBrand(x) → Eco-friendlyBrand(x))

∀x (FastFashionProducts(x) → DisposableProducts(x))

¬HelpSlowDownGlobalWarming(reformation) → Eco-friendlyBrand(reformation) ∨ SustainableFashionBrand(reformation)


Reformation produces fast fashion products.


Reformation does not produce fast fashion products.


Reformation does not produce fast fashion products or does not produce disposable products.


If Reformation produces disposable products, then Reformation produces fast fashion products.


If Reformation produces fast fashion products or helps slow down global warming, then Reformation produces fast fashion products.


Sherville Huggins has never dismissed anyone playing for a constituent country.

Roy Richardson was a cricketer for Sint Maartener, a consituent country.

Roy Richardson was a right handed batsman and medium pace bowler.

Roy Richardson was old when he debuted in cricket.

Sherville Huggins dismissed Roy Richardson.

Cricketeer(royrichardson) ∧ PlayedFor(royrichardson, sintmaartener) ∧ ConstituentCountry(sintmaartener)

RightHanded(royrichardson) ∧ Batsman(royrichardson) ∧ MediumPaceBowler(royrichardson)

Old(royrichardson) ∧ DebutedIn(royrichardson, cricket)


There are no right handed medium pace bowlers playing for Sint Maartener.


To get a job at Google, you need to have a lot of work experience or a good education.

All Yale graduates who submitted their resumes to Google got jobs there.

John submitted his resume to Google and got a job there.

∀x (Employed(x, google) → WorkExp(x) ∨ GoodEduc(x))

∀x ((Yale(x) ∧ CV(x, google)) → Employed(x, google))

CV(john, google) ∧ Employed(john, google)


All graduate students are people taking classes.

If Joe is a graduate student or a doctor (but not both), then Joe is not a graduate student and a student.

∀x (GraduateStudent(x) → TakingClass(x))

GraduateStudent(joe) ⊕  Doctor(joe) → ¬(GraduateStudent(joe) ^ Student(joe))


Hugh Vanstone is one of the world's leading ligting designers and from the uk

Hugh Vanstone is one of the world's leading lighting designers.

Hugh Vanstone has lit more than 160 productions.

Hugh Vanstone attended school where he is from.


Hugh Vanstone attended school in the US.


No man can run faster than Bolt.
Superman is not a man.

∀x (Man(x) → ¬FasterThanBolt(x))
¬Man(superman)


An American scientist has been called the "father of the analysis of algorithms".

Donald Ervin Knuth is an American computer scientist, mathematician, and Professor Emeritus at Stanford University.

Knuth has been called the "father of the analysis of algorithms".

AmericanComputerScientist(donaldErvinKnuth) ∧ Mathematician(donaldErvinKnuth) ∧ ProfessorStanford(donaldErvinKnuth)


A mathematician has been called the "father of the analysis of algorithms".


Donald Knuth is a well-known figure in the field of artificial intelligence .


There is a flea beetle within the Chrysomelidae family.

Neocrepidodera Corpulentas are flea beetles or moths.

The species Neocrepidodera Corpulenta is in the Chrysomelidae family.

There are no moths within the Chrysomelidae family.

Species(neocrepidoderacorpulenta) ∧ Family(chrysomelidae) ∧ In(neocrepidoderacorpulenta, chrysomelidae)

∀x (In(x, chrysomelidae) ∧ Family(chrysomelidae) → ¬Moth(x))


There are no flea beetles within the Chrysomelidae family.


Carrozzeria Colli made car bodies in 1931.

Carrozzeria Colli is a Milanese coachbuilder company that was established by Giuseppe Colli in 1931.

Carrozzeria Colli is a company that specialized in using aluminum.

The first automobiles built by Carrozzeria Colli were racing cars.

Some racing cars built by Carrozzeria Colli used Fiat 1100 mechanicals and chasis.

MilaneseCoachbuilderCompany(carrozzeriacolli) ∧ EstablishedBy(carrozzeriacolli, giuseppecolli) ∧ EstablishedIn(carrozzeriacolli, y1901)

∀x (FirstAutomobilesBy(x, carrozzeriacolli) → Racingcar(x))

∃x (RacingCar(x) ∧ BuiltBy(x, carrozzeriacolli) ∧ Used(x, fiat110mechanicals) ∧ Used(x, chasis))

∃x (Airforce(x) ∧ WorkedFor(carrozzeriacolli, x))


Carrozzeria Colli built airplanes during World War II.


Giuseppe Colli established a company that made car bodies.


Giuseppe Colli established a Milanese coachbuilder company that specialized in using aluminum.


The first automobiles built by Carrozzeria Colli were built using Fiat 1100 mechanicals and chasis.


John will go to the cinema if and only if Jack goes to the cinema today.

Jack will go to the cinema if and only if Iron Man is on and the weather is not bad today.

GoToTheCinema(john, today) ↔ GoToTheCinema(jack, today)

GoToTheCinema(jack, today) ↔ (Movie(ironman) ∧ ¬BadWeather(today))


Quiksilver sells sportswear, clothing, footwear, and accessories.

∀x (QuiksilverSells(x) → Sportswear(x) ∨ Clothing(x) ∨ Footwear(x) ∨ Accessory(x))


Joe owns at least one a piece of sportswear, clothing, footwear, or accessory