TASK DEFINITION: In this task, you are given a context, a subject, a relation, and many options. Based on the context, from the options select the object entity that has the given relation with the subject. Answer with text (not indexes).
PROBLEM: Context: Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum., In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found. Conjectures such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (which was a conjecture until proven in 1995) have shaped much of mathematical history as new areas of mathematics are developed in order to prove them., The Riemann zeta function or EulerRiemann zeta function, , is a function of a complex variable "s" that analytically continues the sum of the Dirichlet series , In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . It was proposed by , after whom it is named. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields., A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which proceed by listing the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions., A complex number is a number that can be expressed in the form , where and are real numbers and is the imaginary unit, satisfying the equation . In this expression, is the ' and is the ' of the complex number. If formula_1, then formula_2, In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod when is a prime number., In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation., In mathematics , the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and Generalized Riemann hypothesis . It states that the nontrivial zeros of all automorphic L - functions lie on the critical line 1/2 + it with t a real number variable and i the imaginary unit . The modified grand Riemann hypothesis is the assertion that the nontrivial zeros of all automorphic L - functions lie on the critical line or the real line ., Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework., Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics., The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function. One can then ask the same question about the zeros of these "L"-functions, yielding various generalizations of the Riemann hypothesis. Many mathematicians believe these generalizations of the Riemann hypothesis to be true. The only cases of these conjectures which have been proven occur in the function field case (not the number field case)., Subject: grand riemann hypothesis, Relation: instance_of, Options: (A) class (B) complex (C) complex number (D) conjecture (E) definition (F) division (G) equation (H) field (I) function (J) hypothesis (K) magnitude (L) mathematics (M) may (N) number (O) order (P) phrase (Q) plane (R) position (S) prime number (T) quantity (U) relation (V) relationship (W) series (X) space (Y) statement (Z) structure ([) study (\) sum (]) term (^) theorem (_) three (`) time (a) unit of measurement (b) variable

SOLUTION: conjecture

PROBLEM: Context: John Bryan Bowman (October 16, 1824  September 21, 1891) was an American lawyer and educator, most notably as the founder Kentucky University and the Agricultural and Mechanical College of Kentucky. He was the grandson of Kentucky frontiersman Abraham Bowman, as well as the grandnephew of Isaac, Joseph and John Jacob Bowman. His great-grandfathers were noted Virginia colonists George Bowman and Jost Hite., Amherst is a town in Erie County, New York, United States. As of the 2010 census, the town had a total population of 122,366. This represents an increase of 5.0% from the 2000 census., A doctorate (from Latin "docere", "to teach") or doctor's degree (from Latin "doctor", "teacher") or doctoral degree (from the ancient formalism "licentia docendi") is an academic degree awarded by universities that is, in most countries, a research degree that qualifies the holder to teach at the university level in the degree's field, or to work in a specific profession. There are a variety of doctoral degrees, with the most common being the Doctor of Philosophy (PhD), which is awarded in many different fields, ranging from the humanities to the scientific disciplines. There are also some doctorates in the US, such as the Juris Doctor (JD), Doctor of Nursing Practice (DNP) and the Doctor of Medicine (MD), which are generally regarded internationally as professional degrees rather than doctorates, as they are not research degrees and no defense of any dissertation or thesis is performed. Many universities also award "honorary doctorates" to individuals who have been deemed worthy of special recognition, either for scholarly work or for other contributions to the university or to society., Kentucky, officially the Commonwealth of Kentucky, is a state located in the east south-central region of the United States. Kentucky is one of four U.S. states constituted as a commonwealth (the others being Virginia, Pennsylvania, and Massachusetts). Originally a part of Virginia, in 1792 Kentucky became the 15th state to join the Union. Kentucky is the 37th most extensive and the 26th most populous of the 50 United States., The University of Kentucky (UK) is a public co-educational university in Lexington, Kentucky. Founded in 1865 by John Bryan Bowman as the "Agricultural and Mechanical College of Kentucky", the university is one of the state's two land-grant universities (the other being Kentucky State University), the largest college or university in the state, with 30,720 students as of Fall 2015, and the highest ranked research university in the state according to "U.S. News and World Report"., Psychology is the study of behavior and mind, embracing all aspects of conscious and unconscious experience as well as thought. It is an academic discipline and a social science which seeks to understand individuals and groups by establishing general principles and researching specific cases. In this field, a professional or researcher is called a psychologist and can be classified as a social, behavioral, or cognitive scientist. Psychologists attempt to understand the role of mental functions in individual and social behavior, while also exploring the physiological and biological processes that underlie cognitive functions and behaviors.
Psychologists explore behavior and mental processes, including perception, cognition, attention, emotion (affect), intelligence, phenomenology, motivation (conation), brain functioning, and personality. This extends to interaction between people, such as interpersonal relationships, including psychological resilience, family resilience, and other areas. Psychologists of diverse orientations also consider the unconscious mind. Psychologists employ empirical methods to infer causal and correlational relationships between psychosocial variables. In addition, or in opposition, to employing empirical and deductive methods, someespecially clinical and counseling psychologistsat times rely upon symbolic interpretation and other inductive techniques. Psychology has been described as a "hub science", with psychological findings linking to research and perspectives from the social sciences, natural sciences, medicine, humanities, and philosophy.
While psychological knowledge is often applied to the assessment and treatment of mental health problems, it is also directed towards understanding and solving problems in several spheres of human activity. By many accounts psychology ultimately aims to benefit society. The majority of psychologists are involved in some kind of therapeutic role, practicing in clinical, counseling, or school settings. Many do scientific research on a wide range of topics related to mental processes and behavior, and typically work in university psychology departments or teach in other academic settings (e.g., medical schools, hospitals). Some are employed in industrial and organizational settings, or in other areas such as human development and aging, sports, health, and the media, as well as in forensic investigation and other aspects of law., Paranormal events are phenomena described in popular culture, folklore, and other non-scientific bodies of knowledge, whose existence within these contexts is described to lie beyond normal experience or scientific explanation., The Center for Inquiry (CFI) is a nonprofit educational organization. Its primary mission is to foster a secular society based on science, reason, freedom of inquiry, and humanist values. CFI has headquarters in the United States and a number of locations around the world., The Committee for Skeptical Inquiry (CSI), formerly known as the Committee for the Scientific Investigation of Claims of the Paranormal (CSICOP), is a program within the transnational American non-profit educational organization Center for Inquiry (CFI), which seeks to "promote scientific inquiry, critical investigation, and the use of reason in examining controversial and extraordinary claims." It was founded by Paul Kurtz in 1976 as an independent non-profit organization (before merging with CFI as one of its programs in 2015), to counter what he regarded as an uncritical acceptance of, and support for, paranormal claims by both the media and society in general. Its philosophical position is one of scientific skepticism. CSI's fellows have included notable scientists, Nobel laureates, philosophers, psychologists, educators and authors. It is headquartered in Amherst, New York., Paul Kurtz (December 21, 1925  October 20, 2012) was a prominent American skeptic and secular humanist. He has been called "the father of secular humanism". He was Professor Emeritus of Philosophy at the State University of New York at Buffalo, having previously also taught at Vassar, Trinity, and Union colleges, and the New School for Social Research., A psychologist is a professional who evaluates and studies behavior and mental processes (see also psychology). Typically, psychologists must have completed a university degree in psychology, which is a master's degree in some countries and a doctorate in others. This definition of psychologist is non-exclusive; in most jurisdictions, members of other professions (such as counselors and psychiatrists) can also evaluate, diagnose, treat, and study mental processes. Some psychologists, such as clinical and counseling psychologists, provide mental health care, and some psychologists, such as social or organizational psychologists conduct research and provide consultation services., Kentucky State University (KSU ) is a public co-educational university in Frankfort, Kentucky. Founded in 1886 as the State Normal School for Colored Persons, KSU was the second state-supported institution of higher learning in Kentucky. It has a total undergraduate enrollment of 2,025 and a total graduate enrollment of 134., Robert Allen Baker Jr. ( June 27 , 1921 -- August 8 , 2005 ) was an American psychologist , professor of psychology emeritus of the University of Kentucky , skeptic , author , and investigator of ghosts , UFO abductions , lake monsters and other paranormal phenomena . He is the editor of Psychology in the Wry , a collection of satire , and was formerly the co-editor of Approaches , a quarterly journal of contemporary poetry . His satirical and humorous verses have appeared in Vogue , Saturday Review , The Journal of Irreproducible Results , Worm - Runners ' Digest , and other journals . He wrote 15 books and is a Past Fellow of the Committee for Skeptical Inquiry ., Subject: robert a. baker, Relation: place_of_death, Options: (A) amherst (B) amherst , new york (C) bryan (D) buffalo (E) central (F) central region (G) erie county (H) kentucky (I) lexington (J) massachusetts (K) media (L) mission (M) most (N) normal (O) trinity (P) union (Q) virginia (R) york

SOLUTION: lexington

PROBLEM: Context: BBC White City, also known as the BBC Media Village (or W12 within the BBC), is a collection of six buildings occupying a 17-acre site at Wood Lane, White City in West London (W12). All formerly properties of the BBC, several have now closed, with only Broadcast Centre and the Lighthouse currently occupied by BBC staff. The site is a short distance down Wood Lane from the former BBC Television Centre., Buckinghamshire (or ), abbreviated Bucks, is a county in South East England which borders Greater London to the south east, Berkshire to the south, Oxfordshire to the west, Northamptonshire to the north, Bedfordshire to the north east and Hertfordshire to the east., The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a sovereign country in western Europe. Lying off the north-western coast of the European mainland, it includes the island of Great Britain (the name of which is also loosely applied to the whole country), the north-eastern part of the island of Ireland, and many smaller islands. Northern Ireland is the only part of the UK that shares a land border with another sovereign statethe Republic of Ireland. Apart from this land border, the UK is surrounded by the Atlantic Ocean, with the North Sea to its east, the English Channel to its south and the Celtic Sea to its south-south-west, giving it the 12th-longest coastline in the world. The Irish Sea lies between Great Britain and Ireland. With an area of , the UK is the 78th-largest sovereign state in the world and the 11th-largest in Europe. It is also the 21st-most populous country, with an estimated 65.1 million inhabitants. Together, this makes it the fourth most densely populated country in the European Union., Rapid transit, also known as heavy rail, metro, subway, tube, or underground, is a type of high-capacity public transport generally found in urban areas. Unlike buses or trams, rapid transit systems are electric railways that operate on an exclusive right-of-way, which cannot be accessed by pedestrians or other vehicles of any sort, and which is often grade separated in tunnels or on elevated railways., Shepherds Bush Green (also known as Shepherds Bush Common), is an approximately triangular area of open grass surrounded by trees and roads with shops in Shepherd's Bush, an area of west London which takes its name from the Green. The Green is also a ward of the London Borough of Hammersmith and Fulham. The population of the ward at the 2011 Census was 12,175., The BBC Television Centre at White City in west London was the headquarters of BBC Television between 1960 and 2013. Officially opened on 29 June 1960, it is one of the most readily recognisable facilities of its type, having appeared as the backdrop for many BBC programmes. Parts of the building are Grade II listed, including the central ring and Studio 1. Most of the BBC's national television and radio news output came from the Television Centre (TVC) with most recorded television output from the nearby Broadcast Centre at 201 Wood Lane, care of Red Bee Media. Live television events from studios and routing of national and international sporting events took place within the Television Centre before being passed to the Broadcast Centre for transmission., London is the capital and most populous city of England and the United Kingdom, as well as the most populous city proper in the European Union. Standing on the River Thames in the south east of the island of Great Britain, London has been a major settlement for two millennia. It was founded by the Romans, who named it "Londinium". London's ancient core, the City of London, largely retains its medieval boundaries. Since at least the 19th century, "London" has also referred to the metropolis around this core, historically split between Middlesex, Essex, Surrey, Kent, and Hertfordshire, which today largely makes up Greater London, governed by the Mayor of London and the London Assembly., Wormwood Scrubs, known locally as The Scrubs (or simply Scrubs), is an open space located in the north-eastern corner of the London Borough of Hammersmith and Fulham in west London. It is the largest open space in the Borough, at 80 ha (200 acres), and one of the largest areas of common in London. The eastern part, known as Little Wormwood Scrubs, is cut off by Scrubs Lane and the West London Line railway. It has been an open public space since the Wormwood Scrubs Act of 1879., Kent is a county in South East England and one of the home counties. It borders Greater London to the north west, Surrey to the west, East Sussex to the south west, and Essex across the Thames Estuary to the north. The county town is Maidstone. , The City of London is a city and county within London. It constituted most of London from its settlement by the Romans in the 1st century AD to the Middle Ages, but the agglomeration has since grown far beyond the City's borders. The City is now only a tiny part of the metropolis of London, though it remains a notable part of central London. Administratively, it forms one of the 33 local authority districts of Greater London; however, the City of London is not a London borough, a status reserved for the other 32 districts (including London's only other city, the City of Westminster). , Londinium was a settlement established on the current site of the City of London around  43. Its bridge over the River Thames turned the city into a road nexus and major port, serving as a major commercial centre in Roman Britain until its abandonment during the 5th century., England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west. The Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain (which lies in the North Atlantic) in its centre and south; and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight., Great Britain, also known as Britain , is a large island in the north Atlantic Ocean off the northwest coast of continental Europe. With an area of , Great Britain is the largest European island and the ninth-largest in the world. In 2011 the island had a population of about 61 million people, making it the world's third-most populous island after Java in Indonesia and Honshu in Japan. The island of Ireland is situated to the west of it, and together these islands, along with over 1,000 smaller surrounding islands, comprise the British Isles archipelago., Surrey is a county in the south east of England and also one of the home counties bordering Greater London. Surrey shares borders with Kent to the east, East Sussex to the south-east, West Sussex to the south, Hampshire to the west and south-west and Berkshire to the north-west. The county town is Guildford. Surrey County Council sits extraterritorially at Kingston upon Thames, administered as part of Greater London since 1965. With a resident population of 1.1 million, Surrey is the most densely populated and third most populated county in the South East region, after Kent and Hampshire., Loftus Road Stadium is a football stadium in Shepherd's Bush, London, which is home to Queens Park Rangers. In 1981, the ground became the first stadium in British professional football to have an artificial pitch of Omniturf installed, which remained until 1988., The River Thames is a river that flows through southern England. At , it is the longest river entirely in England and the second longest in the United Kingdom, after the River Severn. It also flows through Oxford (where it is called Isis), Reading, Henley-on-Thames and Windsor. The lower reaches of the river are called the Tideway, derived from its long tidal reach up to Teddington Lock. It rises at Thames Head in Gloucestershire, and flows into the North Sea via the Thames Estuary. The Thames drains the whole of Greater London. , The London Assembly is an elected body, part of the Greater London Authority, that scrutinises the activities of the Mayor of London and has the power, with a two-thirds majority, to amend the Mayor's annual budget and to reject the Mayor's draft statutory strategies. The assembly was established in 2000 and meets at City Hall on the South Bank of the River Thames, close to Tower Bridge. The assembly is also able to investigate other issues of importance to Londoners (transport, environmental matters, etc.), publish its findings and recommendations, and make proposals to the Mayor., Wood Lane (A219, formerly A40) is a street in London. It runs north from Shepherd's Bush, under the Westway (A40) past Wormwood Scrubs where it meets Scrubs Lane. The road is wholly in the London Borough of Hammersmith and Fulham (W12 postal district). It is probably best known as the home of the iconic BBC Television Centre, also BBC White City and formerly BBC Woodlands the offices of BBC Worldwide., Middlesex (abbreviation: Middx) was a county in southeast England that is now mostly part of Greater London, with small sections in neighbouring counties. It was established in the Anglo-Saxon system from the territory of the Middle Saxons, and existed as an official unit until 1965. The historic county included land stretching north of the River Thames from east to west of the City of London with the rivers Colne and Lea and a ridge of hills as the other boundaries. The largely low-lying county, dominated by clay in its north and alluvium on gravel in its south, was the second smallest by area in 1831., The London Borough of Hammersmith and Fulham is a London borough in West London, and forms part of Inner London. Traversed by the east-west main roads of the A4 Great West Road and the A40 Westway, many international corporations have offices in the borough. The local council is Hammersmith and Fulham London Borough Council. The borough is unique in London in having three professional football clubs, Chelsea, Fulham and Queens Park Rangers., The Mayor of London is an elected politician who, along with the London Assembly of 25 members, is accountable for the strategic government of Greater London. The current mayor is Sadiq Khan, who took up office on 9 May 2016. The position had been held by Ken Livingstone from the creation of the role on 4 May 2000 until he was defeated in 2008 by Boris Johnson, who served two terms before being succeeded by Khan., The London Underground (also known simply as the Underground, or by its nickname the Tube) is a public rapid transit system serving Greater London and some parts of the adjacent counties of Buckinghamshire, Essex and Hertfordshire in the United Kingdom., Wood Lane is a London Underground station in the White City area of west London , United Kingdom . It is on the Circle and Hammersmith & City lines , between Latimer Road and Shepherd 's Bush Market stations , in Travelcard Zone 2 . Although it is on a line which has been in operation since 1864 , the station is new , having opened in 2008 . It is near the site of a station of the same name that closed in 1959 ., Hertfordshire (often abbreviated Herts) is a county in southern England, bordered by Bedfordshire to the north, Cambridgeshire to the north-east, Essex to the east, Buckinghamshire to the west and Greater London to the south. For government statistical purposes, it is placed in the East of England region., Shepherd's Bush is an area of west London in the London Borough of Hammersmith and Fulham. Although it is primarily residential in character, its focus is the shopping area of Shepherd's Bush Green, with the Westfield shopping centre lying a short distance to the north. The main thoroughfares are Uxbridge Road, Goldhawk Road and Askew Road, all containing a large number of small and mostly independent shops, pubs and restaurants. The Loftus Road football stadium in Shepherd's Bush is home to Queens Park Rangers. In 2011, the population of the area was 39,724. , The European Union (EU) is a political and economic union of member states that are located primarily in Europe. It has an area of , and an estimated population of over 510 million. The EU has developed an internal single market through a standardised system of laws that apply in all member states. EU policies aim to ensure the free movement of people, goods, services, and capital within the internal market, enact legislation in justice and home affairs, and maintain common policies on trade, agriculture, fisheries, and regional development. Within the Schengen Area, passport controls have been abolished. A monetary union was established in 1999 and came into full force in 2002, and is composed of 19 EU member states which use the euro currency., Hammersmith is a district in west London, located in the London Borough of Hammersmith and Fulham., BBC Worldwide Ltd. is the wholly owned commercial subsidiary of the BBC, formed out of a restructuring of its predecessor BBC Enterprises in 1995. The company monetises BBC brands, selling BBC and other British programming for broadcast abroad with the aim of supplementing the income received by the BBC through the licence fee., Subject: wood lane tube station, Relation: located_in_the_administrative_territorial_entity, Options: (A) atlantic ocean (B) berkshire (C) buckinghamshire (D) centre (E) chelsea (F) city of westminster (G) colne (H) district (I) east of england (J) england (K) eu (L) europe (M) european union (N) fulham (O) greater london (P) guildford (Q) hampshire (R) hertfordshire (S) ireland (T) japan (U) java (V) kent (W) kingston (X) kingston upon thames (Y) loftus (Z) london ([) london borough of hammersmith and fulham (\) mainland (]) media (^) middlesex (_) news (`) north (a) north east (b) northamptonshire (c) northern (d) northwest (e) of (f) oxford (g) oxfordshire (h) reading (i) river (j) schengen (k) south (l) stadium (m) street (n) surrey (o) united kingdom (p) west (q) westminster (r) windsor (s) woodlands

SOLUTION:
london borough of hammersmith and fulham