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).

Context: Monica Vitti (born 3 November 1931) is an Italian actress best known for her starring roles in films directed by Michelangelo Antonioni during the early 1960s. After working with Antonioni, Vitti changed focus and began making comedies, working with director Mario Monicelli on many films. She has appeared opposite Marcello Mastroianni, Richard Harris, Terence Stamp, Michael Caine and Dirk Bogarde. Vitti won five David di Donatello Awards for Best Actress, seven Italian Golden Globes for Best Actress, the Career Golden Globe, and the Venice Film Festival Career Golden Lion Award., Rome is a city and special "comune" (named "Roma Capitale") in Italy. Rome is the capital of Italy and of the Lazio region. With 2,870,336 residents in , it is also the country's largest and most populated "comune" and fourth-most populous city in the European Union by population within city limits. The Metropolitan City of Rome has a population of 4.3 million residents. The city is located in the central-western portion of the Italian Peninsula, within Lazio (Latium), along the shores of Tiber river. The Vatican City is an independent country geographically located within the city boundaries of Rome, the only existing example of a country within a city: for this reason Rome has been often defined as capital of two states. , A screenplay writer, screenwriter for short, scriptwriter or scenarist is a writer who practices the craft of screenwriting, writing screenplays on which mass media such as films, television programs, comics or video games are based., MILAN ("milan(e)" is French for kite) is a European anti-tank guided missile. Design of the MILAN started in 1962, it was ready for trials in 1971, and was accepted for service in 1972. It is a wire guided SACLOS (semi-automatic command to line-of-sight) missile, which means the sight of the launch unit has to be aimed at the target to guide the missile. The MILAN can be equipped with a MIRA or MILIS thermal sight to give it night-firing ability., A writer is a person who uses written words in various styles and techniques to communicate their ideas. Writers produce various forms of literary art and creative writing such as novels, short stories, poetry, plays, screenplays, and essays as well as various reports and news articles that may be of interest to the public. Writers' texts are published across a range of media. Skilled writers who are able to use language to express ideas well often contribute significantly to the cultural content of a society. The word is also used elsewhere in the arts  such as songwriter  but as a standalone term, "writer" normally refers to the creation of written language. Some writers work from an oral tradition., Sicily is the largest island in the Mediterranean Sea. It constitutes an autonomous Region of Italy, along with surrounding minor islands, officially referred to as "Regione Siciliana" (in Italian, Sicilian Region)., A stockbroker is a regulated professional individual, usually associated with a brokerage firm or broker-dealer, who buys and sells stocks and other securities for both retail and institutional clients through a stock exchange or over the counter in return for a fee or commission. Stockbrokers are known by numerous professional designations, depending on the license they hold, the type of securities they sell, or the services they provide. In the United States, a stockbroker must pass both the Series 7 and either the Series 63 or the Series 66 exams in order to be properly licensed., L'Avventura is a 1960 Italian film directed by Michelangelo Antonioni and starring Gabriele Ferzetti, Monica Vitti, and Lea Massari. Developed from a story by Antonioni, the film is about a young woman's disappearance during a Mediterranean boating trip. Her lover and her best friend, during the subsequent search for her, become attracted to each other. The film is noted for its careful pacing, which puts a focus on visual composition and character development, as well as for its unusual narrative structure. According to an Antonioni obituary, the film "systematically subverted the filmic codes, practices and structures in currency at its time." Filmed on location in Rome, the Aeolian Islands, and Sicily in 1959 under difficult financial and physical conditions, "L'Avventura" made Monica Vitti an international star. The film was nominated for numerous awards and was awarded the Jury Prize at the 1960 Cannes Film Festival. "L'Avventura" is the first film of a trilogy by Antonioni, followed by "La Notte" (1961) and "L'Eclisse" (1962)., A trilogy (from Greek - "", "three" and - "-logia", "discourse") is a set of three works of art that are connected, and that can be seen either as a single work or as three individual works. They are commonly found in literature, film, or video games. Three-part works that are considered components of a larger work also exist, such as the triptych or the three-movement sonata, but they are not commonly referred to with the term "trilogy.", La Notte is a 1961 Italian drama film directed by Michelangelo Antonioni and starring Marcello Mastroianni, Jeanne Moreau and Monica Vitti (Umberto Eco appeared in a cameo). Filmed on location in Milan, the film is about a day in the life of an unfaithful married couple and their deteriorating relationship. In 1961 "La Notte" received the Golden Bear at the Berlin International Film Festival, as well as the David di Donatello Award for Best Director. "La Notte" is considered the central film of a trilogy beginning with "L'Avventura" (1960) and ending with "L'Eclisse" (1962)., Michelangelo Antonioni , Cavaliere di Gran Croce OMRI ( 29 September 1912 -- 30 July 2007 ) , was an Italian film director , screenwriter , editor , and short story writer . Best known for his `` trilogy on modernity and its discontents '' -- L'Avventura ( 1960 ) , La Notte ( 1961 ) , and L'Eclisse ( 1962 ) -- Antonioni `` redefined the concept of narrative cinema '' and challenged traditional approaches to storytelling , realism , drama , and the world at large . He produced `` enigmatic and intricate mood pieces '' and rejected action in favor of contemplation , focusing on image and design over character and story . His films defined a `` cinema of possibilities '' . Antonioni received numerous awards and nominations throughout his career , including the Cannes Film Festival Jury Prize ( 1960 , 1962 ) , Palme d'Or ( 1966 ) , and 35th Anniversary Prize ( 1982 ) ; the Venice Film Festival Silver Lion ( 1955 ) , Golden Lion ( 1964 ) , FIPRESCI Prize ( 1964 , 1995 ) , and Pietro Bianchi Award ( 1998 ) ; the Italian National Syndicate of Film Journalists Silver Ribbon eight times ; and an honorary Academy Award in 1995 ., Alain Fabien Maurice Marcel Delon (born 8 November 1935) is a French-Swiss actor and businessman. Delon became one of Europe's most prominent actors and screen sex symbols in the 1960s. He achieved critical acclaim for roles in films such as "Rocco and His Brothers" (1960), "Purple Noon" (1960), "L'Eclisse" (1962), "The Leopard" (1963), "Lost Command" (1966) and "Le Samouraï" (1967). Over the course of his career Delon worked with many well-known directors, including Luchino Visconti, Jean-Luc Godard, Jean-Pierre Melville, Michelangelo Antonioni and Louis Malle., Jeanne Moreau (born 23 January 1928) is a French actress, singer, screenwriter and director. She is the recipient of a César Award for Best Actress, a BAFTA Award for Best Foreign Actress and a Cannes Film Festival Best Actress Award for individual performances, and several lifetime awards., Anna Maria Massetani better known as Lea Massari (born 30 June 1933) is an Italian actress and singer., The Aeolian Islands (, , , "Aiolides Nisoi") are a volcanic archipelago in the Tyrrhenian Sea north of Sicily, named after the demigod of the winds Aeolus. The islands' inhabitants are known as Aeolians. The Aeolian Islands are a popular tourist destination in the summer and attract up to 200,000 visitors annually., A film, also called a movie, motion picture, theatrical film or photoplay, is a series of still images which, when shown on a screen, creates the illusion of moving images due to the phi phenomenon. This optical illusion causes the audience to perceive continuous motion between separate objects viewed rapidly in succession. The process of filmmaking is both an art and an industry. A film is created by photographing actual scenes with a motion picture camera; by photographing drawings or miniature models using traditional animation techniques; by means of CGI and computer animation; or by a combination of some or all of these techniques and other visual effects., A film director is a person who directs the making of a film. Generally, a film director controls a film's artistic and dramatic aspects, and visualizes the script while guiding the technical crew and actors in the fulfillment of that vision. The director has a key role in choosing the cast members, production design, and the creative aspects of filmmaking. Under European Union law, the director is viewed as the author of the film., 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., The David di Donatello Award, named after Donatello's "David", is a film award presented each year for cinematic performances and production by L'accademia del Cinema Italiano (ACI). There are 24 categories as of 2006. Italy is also famed for its annual Venice Film Festival., The Golden Bear is the highest prize awarded for the best film at the Berlin International Film Festival. The bear is the heraldic animal of Berlin, featured on both the coat of arms and flag of Berlin., The history of comics has followed different paths in different cultures. Scholars have posited a pre-history as far back as the Lascaux cave paintings. By the mid-20th century, comics flourished particularly in the United States, western Europe (especially in France and Belgium), and Japan. The history of European comics is often traced to Rodolphe Töpffer's cartoon strips of the 1830s, and became popular following the success in the 1930s of strips and books such as "The Adventures of Tintin". American comics emerged as a mass medium in the early 20th century with the advent of newspaper comic strips; magazine-style comic books followed in the 1930s, in which the superhero genre became prominent after Superman appeared in 1938. Histories of Japanese comics and cartooning ("") propose origins as early as the 12th century. Modern comic strips emerged in Japan in the early 20th century, and the output of comics magazines and books rapidly expanded in the post-World War II era with the popularity of cartoonists such as Osamu Tezuka. had a lowbrow reputation for much of its history, but towards the end of the 20th century began to find greater acceptance with the public and in academia., A screenplay or script is a written work by screenwriters for a film, video game, or television program. These screenplays can be original works or adaptations from existing pieces of writing. In them, the movement, actions, expression, and dialogues of the characters are also narrated. A screenplay written for television is also known as a teleplay., Screenwriting, also called scriptwriting, is the art and craft of writing scripts for mass media such as feature films, television productions or video games. It is frequently a freelance profession., Martin Charles Scorsese (born November 17, 1942) is an American director, producer, screenwriter, actor, and film historian, whose career spans more than 53 years. Scorsese's body of work addresses such themes as Sicilian-American identity, Roman Catholic concepts of guilt and redemption, faith, machismo, modern crime, and gang conflict. Many of his films are also known for their depiction of violence and liberal use of profanity., My Voyage to Italy is a personal documentary by acclaimed Italian-American director Martin Scorsese. The film is a voyage through Italian cinema history, marking influential films for Scorsese and particularly covering the Italian neorealism period., The 15th Cannes Film Festival was held on May 723, 1962. The Palme d'Or went to the "O Pagador de Promessas" by Anselmo Duarte. The festival opened with "Les Amants de Teruel", directed by Raymond Rouleau., A television program is a segment of content intended for broadcast on over-the-air, cable television, or Internet television, other than a commercial, trailer, or any other segment of content not serving as attraction for viewership. It may be a single production, or more commonly, a series of related productions (also called a television series or a television show)., Gabriele Ferzetti (born Pasquale Ferzetti; 17 March 1925  2 December 2015) was an Italian actor with more than 160 credits to his name across film, television, and stage. His career was at its peak in the 1950s and 1960s., The 13th Cannes Film Festival was held from 4 to 20 May 1960. The Palme d'Or went to the "La Dolce Vita" by Federico Fellini. The festival opened with "Ben-Hur", directed by William Wyler., Marcello Vincenzo Domenico Mastroianni, Knight Grand Cross (28 September 1924  19 December 1996) was an Italian film actor. His prominent films include: "La Dolce Vita"; "8"; "La Notte"; "Divorce, Italian Style"; "Yesterday, Today and Tomorrow"; "Marriage Italian-Style"; "The 10th Victim"; "A Special Day"; "City of Women"; "Henry IV"; "Dark Eyes"; and "Stanno tutti bene". His honours included British Film Academy Awards, Best Actor awards at the Cannes Film Festival and two Golden Globe Awards., Umberto Eco (5 January 1932  19 February 2016) was an Italian novelist, literary critic, philosopher, semiotician, and university professor. He is best known internationally for his 1980 novel "Il nome della rosa" ("The Name of the Rose"), a historical mystery combining semiotics in fiction with biblical analysis, medieval studies, and literary theory. He later wrote other novels, including "Il pendolo di Foucault" ("Foucault's Pendulum") and "L'isola del giorno prima" ("The Island of the Day Before"). His novel "Il cimitero di Praga" ("The Prague Cemetery"), released in 2010, was a best-seller., L'Eclisse is a 1962 Italian drama film written and directed by Michelangelo Antonioni and starring Alain Delon and Monica Vitti. Filmed on location in Rome and Verona, "L'Eclisse" is about a young woman who breaks up with an older lover and then has an affair with a confident young stockbroker whose materialistic nature eventually undermines their relationship. The film is considered the last part of a trilogy which was preceded by "L'Avventura" (1960) and "La Notte" (1961). In Martin Scorsese's documentary "My Voyage to Italy", the director called "L'Eclisse" the boldest film in Antonioni's trilogy. "L'Eclisse" won the Special Jury Prize at the 1962 Cannes Film Festival and was nominated for the "Palme d'Or"., Subject: michelangelo antonioni, Relation: given_name, Options: (A) alain (B) an (C) anna (D) are (E) art (F) ben (G) berlin (H) can (I) cave (J) charles (K) césar (L) david (M) della (N) domenico (O) duarte (P) faith (Q) foucault (R) france (S) french (T) gabriele (U) henry (V) january (W) jean (X) jeanne (Y) june (Z) line ([) marcel (\) marcello (]) maria (^) martin (_) maurice (`) may (a) michael (b) michelangelo (c) milan (d) mira (e) monica (f) my (g) omri (h) rocco (i) roma (j) rosa (k) rose (l) set (m) stamp (n) terence (o) umberto (p) verona (q) vincenzo (r) vita (s) young
michael

Context: Abaye was a rabbi of the Jewish Talmud who lived in Babylonia [], known as an amora [] born about the close of the third century; died 339 CE (see Talmudic Academies in Babylonia). His father, Kaylil, was the brother of Rabbah bar Nachmani, a teacher at the Academy of Pumbedita. Abaye's real name was Nachmani, after his grandfather. Left an orphan at an early age, he was adopted by his uncle, Rabbah bar Nachmani, who nicknamed him Abaye ("Little Father"), to avoid confusion (perhaps respect for his father) with his grandfather of the same name; thenceforth he was known as Abaye, without any other title. It is a curious fact that he perpetuated the memory of his foster-mother by mentioning her name in many popular recipes and dietetic precepts, some of which seem to be based on superstitious notions. He introduced each recipe with the phrase, "My mother told me." Abaye's teachers were his uncle Rabbah and Joseph bar Chama, both of whom successively became presidents of the Pumbedita Academy. When Joseph died (324 CE), this dignity was conferred upon Abaye, who retained it until his death some five years later. Rabbah trained him in the application of the dialectic method to halakhic problems, and Joseph, with his stores of traditional lore, taught him to appreciate the value of positive knowledge., Abba Arikha (175247) (Talmudic Aramaic: ; born: "Abba bar Aybo", Hebrew:    ) was a Jewish Talmudist who was born and lived in Kafri, Sassanid Babylonia, known as an amora (commentator on the Oral Law) of the 3rd century who established at Sura the systematic study of the rabbinic traditions, which, using the "Mishnah" as text, led to the compilation of the "Talmud". With him began the long period of ascendancy of the great academies of Babylonia , around the year 220. He is commonly known simply as Rav (or Rab, Hebrew: )., The Tigris is the eastern member of the two great rivers that define Mesopotamia, the other being the Euphrates. The river flows south from the mountains of southeastern Turkey through Iraq and empties itself into the Persian Gulf., The Akkadian Empire was the first ancient Semitic-speaking empire of Mesopotamia, centered in the city of Akkad and its surrounding region, also called Akkad in ancient Mesopotamia and Accad in the Bible (Genesis 10:10). The empire united all the Akkadian and Sumerian speakers under one rule. The Akkadian Empire controlled Mesopotamia (modern Iraq, Kuwait, northeast Syria and southeast Turkey), the Levant (modern Syria and Lebanon), and eastern and southern parts of Anatolia (modern Turkey) and Iran, sending military expeditions as far south as Dilmun and Magan (modern Bahrain and Oman) in the Arabian Peninsula., Exilarch (Hebrew:   "Rosh Galut", Aramaic:   "Reysh Galuta" or "Resh Galvata" lit. "head of the exile", Arabic:   "Raas al-Galut", Greek:  "Aechmalotarches" lit. "leader of the captives") refers to the leaders of the Diaspora Jewish community in Babylon following the deportation of King Jeconiah and his court into Babylonian exile after the first fall of Jerusalem in 597 BCE and augmented after the further deportations following the destruction of the kingdom of Judah in 587 BCE. The people in exile were called "golah" or "galut"., A city is a large and permanent human settlement. Although there is no agreement on how a city is distinguished from a town in general English language meanings, many cities have a particular administrative, legal, or historical status based on local law., An oral law is a code of conduct in use in a given culture, religion or community application, by which a body of rules of human behaviour is transmitted by oral tradition and effectively respected, or the single rule that is orally transmitted., The Mishnah or Mishna ("study by repetition"), from the verb "shanah" , or "to study and review", also "secondary", is the first major written redaction of the Jewish oral traditions known as the "Oral Torah". It is also the first major work of Rabbinic literature., Hai ben Sherira (or Hai b. Sherira (Gaon), Hebrew:   ; better known as Hai Gaon, Hebrew:  ), was a medieval Jewish theologian, rabbi and scholar who served as Gaon of the Talmudic academy of Pumbedita during the early 11th century. He was born in 939 and died on March 28, 1038. He received his Talmudic education from his father, Sherira ben Hanina, and in early life acted as his assistant in teaching. In his forty-fourth year he became associated with his father as ""ab bet din"," and with him delivered many joint decisions., For the fourth generation Amora of Babylon , see Rabbah b. Shela . Shela ( Hebrew :   ) was a Babylonian teacher of the latter part of the tannaitic and the beginning of the amoraic period , and head of the school ( `` sidra '' ) at Nehardea ( Yoma 20a ; Letter of Sherira Gaon , in Neubauer , M. J. C. i. 28 ) . When Abba Arika ( Rab ) visited Babylon , he once officiated as an expounder ( amora ) for R. Shela at his public lectures ( Yoma l.c . ) . The school at Nehardea was named in honor of Shela ; and its scholars were accordingly known as `` D'Bei R. Shela . '' With the exception of a mishnaic interpretation ( Yoma 20a ) , none of Shela 's teachings is known , although some of the sayings of the students of his academy , the Bei R. Shela , are mentioned in the Talmud ( Pes . 39b ; R. H. 23b ; Gi . 52b ; id . 43a ) ., Babylonia was an ancient Akkadian-speaking state and cultural area based in central-southern Mesopotamia (present-day Iraq). A small Amorite-ruled state emerged in 1894 BC, which contained at this time the minor city of Babylon. Babylon greatly expanded during the reign of Hammurabi in the first half of the 18th century BC, becoming a major capital city. During the reign of Hammurabi and afterwards, Babylonia was called "Mt Akkad" "the country of Akkad" in the Akkadian language.
It was often involved in rivalry with its older fellow Akkadian-speaking state of Assyria in northern Mesopotamia. Babylonia briefly became the major power in the region after Hammurabi (fl. c. 1792  1752 BC middle chronology, or c. 1696  1654 BC, short chronology) created a short-lived empire, succeeding the earlier Akkadian Empire, Third Dynasty of Ur, and Old Assyrian Empire; however, the Babylonian empire rapidly fell apart after the death of Hammurabi., Rav Sherira Gaon (Hebrew:    or R. Sherira Gaon bar anina , Hebrew:      or merely Sherira b. anina) was the head (gaon) of the Academy of Pumbeditha. He was one of the most prominent Geonim of his period, and the father of Hai Gaon, who succeeded him as gaon., Babylon (or ; Aramaic: , "Babel", , "Bavel", , "Bbil") was a major city of ancient Mesopotamia in the fertile plain between the Tigris and Euphrates rivers. The city was built upon the Euphrates and divided in equal parts along its left and right banks, with steep embankments to contain the river's seasonal floods. Babylon was originally a small Semitic Akkadian city dating from the period of the Akkadian Empire c. 2300 BC., Jerusalem , is a city located on a plateau in the Judaean Mountains between the Mediterranean and the Dead Sea. One of the oldest cities in the world, Jerusalem was named as ""Urusalima"" on ancient Mesopotamian cuneiform tablets, probably meaning "City of Shalem" after a Canaanite deity, during the early Canaanite period (approximately 2400 BCE). During the Israelite period, significant construction activity in Jerusalem began in the 9th century BCE (Iron Age II), and in the 8th century the city developed into the religious and administrative center of the Kingdom of Judah. It is considered a holy city in the three major Abrahamic religions of Judaism, Christianity and Islam., Nehardea or Nehardeah ("river of knowledge") was a city of Babylonia, situated at or near the junction of the Euphrates with the Nahr Malka (also known as Nâr Sharri, Ar-Malcha, Nahr el-Malik, and King's Canal), one of the earliest centers of Babylonian Judaism. As the seat of the exilarch it traced its origin back to King Jehoiachin. According to Sherira Gaon (Letter of Sherira Gaon, in Neubauer, "M. J. C." i. 26), Jehoiachin and his coexilarchs built a synagogue at Nehardea, for the foundation of which they used earth and stones which they had brought, in accordance with the words of Psalms 102:15, from Jerusalem (comp. a similar statement in regard to the founding of the Jewish neighbourhood in the Persian city of Ispahan, in "Monatsschrift," 1873, pp. 129, 181). For this reason it was called 'The Synagogue that Slid and Settled'. This was the synagogue called "Shaf we-Yatib," to which there are several references dating from the third and fourth centuries (R. H. 24b; Avodah Zarah 43b; Niddah 13a), and which Abaye asserts (Meg. 29a) was the seat of the Shekhinah in Babylonia. The Aaronic portion of the Jewish population of Nehardea was said to be descended from the slaves of Pashur ben Immer, the contemporary of King Jehoiachin (Kiddushin 70b)., The Talmud (Hebrew: ' "instruction, learning", from a root ' "teach, study") is a central text of Rabbinic Judaism. It is also traditionally referred to as, a Hebrew abbreviation of ', the "six orders", a reference to the six orders of the Mishnah. The term "Talmud" normally refers to the collection of writings named specifically the Babylonian Talmud "(Talmud Bavli)", although there is also an earlier collection known as the Jerusalem Talmud, or Palestinian Talmud"' "(Talmud Yerushalmi)". When referring to post-biblical periods, namely those of the creation of the Talmud, the Talmudic academies and the Babylonian exilarchate, Jewish sources use the term "Babylonia" long after it had become obsolete in geopolitical terms., The Book of Psalms (or , "Tehillim", "praises"), commonly referred to simply as Psalms or "the Psalms", is the first book of the "Ketuvim" ("Writings"), the third section of the Hebrew Bible, and a book of the Christian Old Testament. The title is derived from the Greek translation,  "psalmoi", meaning "instrumental music" and, by extension, "the words accompanying the music." The book is an anthology of individual psalms, with 150 in the Jewish and Western Christian tradition and more in the Eastern Christian churches. Many of the psalms are linked to the name of King David, although his authorship is not accepted by some modern Bible scholars., Akkadian ("akkadû", ak-ka-du-u; logogram: URI ) is an extinct East Semitic language (part of the greater Afroasiatic language family) that was spoken in ancient Mesopotamia. The earliest attested Semitic language, it used the cuneiform writing system, which was originally used to write the unrelated Ancient Sumerian, a language isolate. The language was named after the city of Akkad, a major centre of Mesopotamian civilization during the Akkadian Empire (ca. 23342154 BC), but the language itself precedes the founding of Akkad by many centuries., Subject: rav shela, Relation: occupation, Options: (A) book (B) construction (C) general (D) king (E) leader (F) major (G) member (H) military (I) r (J) rabbi (K) religion (L) religious (M) talmudist (N) teach (O) teacher (P) theologian (Q) translation (R) writing system
rabbi

Context: 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., 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 neuropsychology, linguistics and the philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages can take different forms, such as speech, signing, or writing. They are distinguished from constructed and formal languages such as those used to program computers or to study logic., In mathematics , and more specifically in naive set theory , the domain of definition ( or simply the domain ) of a function is the set of `` input '' or argument values for which the function is defined . That is , the function provides an `` output '' or value for each member of the domain . Conversely , the set of values the function takes on as output is termed the image of the function , which is sometimes also referred to as the range of the function . For instance , the domain of cosine is the set of all real numbers , while the domain of the square root consists only of numbers greater than or equal to 0 ( ignoring complex numbers in both cases ) . When the domain of a function is a subset of the real numbers , and the function is represented in an xy Cartesian coordinate system , the domain is represented on the x-axis ., Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects., 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., 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., Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using a formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday usage of set theory concepts in contemporary mathematics., Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague.
Foundations of mathematics can be conceived as the study of the basic mathematical concepts (number, geometrical figure, set, function, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges., A Venn diagram (also called a set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled "S" represent elements of the set "S", while points outside the boundary represent elements not in the set "S". Thus, for example, the set of all elements that are members of both sets "S" and "T", "S""T", is represented visually by the area of overlap of the regions "S" and "T". In Venn diagrams the curves are overlapped in every possible way, showing all possible relations between the sets. They are thus a special case of Euler diagrams, which do not necessarily show all relations. Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics and computer science., Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics  such as integers, graphs, and statements in logic  do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions., Subject: domain of a function, Relation: instance_of, Options: (A) algebra (B) area (C) boolean algebra (D) branch (E) change (F) complex (G) computer (H) concept (I) definition (J) diagram (K) direction (L) four (M) framework (N) function (O) humans (P) language (Q) logic (R) magnitude (S) mathematics (T) may (U) natural language (V) ordinary (W) part (X) philosophy (Y) phrase (Z) planning ([) property (\) quality (]) quantity (^) science (_) sense (`) set (a) set theory (b) show (c) space (d) statement (e) study (f) three (g) two (h) word

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