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: Jaclyn Joshua Thanaraj Victor (born 4 December 1978), popularly known as Jaclyn Victor, is a Malaysian singer and actress who won the inaugural "Malaysian Idol" and "Ikon Malaysia". As the winner of "Malaysian Idol", she won a recording contract with Sony BMG Music Entertainment. She is under the management of The 8 Unit. She represented Malaysia in the first "Asian Idol" and "Ikon Asean". She has been dubbed "Asia's Divette" for her vocal prowess., Pop Idol is a British television music competition created by Simon Fuller which ran on ITV from 2001 to 2003. The aim of the show was to decide the best new young pop singer (or "pop idol") in the UK based on viewer voting and participation. Two series were broadcastone in 20012002 and a second in 2003. "Pop Idol" was subsequently put on an indefinite hiatus after series judge Simon Cowell announced the launch of "The X Factor" in the UK in April 2004., Gemilang is an album released in 2005 by Jaclyn Victor , the first Malaysian Idol . This album has eleven tracks , including Tunggu Sekejap , When I Fall in Love and Gemilang , the three songs performed by Jaclyn Victor which eventually led to her winning the inaugural competition ., Malaysian Idol is the Malaysian version of the Idol Series that started in UK, similar to shows such as UK's "Pop Idol" and "American Idol" in the franchise. This show is a contest to determine the best young singer in Malaysia, with the winner receiving a major record deal, although some runners-up have achieved enough fame to ink record deals of their own. Like any other "Idol" show, the winner is decided by public votes. The "Malaysian Idol" series has gained a following in Malaysia from people of all ages partly due to their interest in American Idol which had been introduced a few years prior. Malaysian Idol has been broadcast to Malaysian viewers via terrestrial television, 8TV and TV3., IKON Malaysia is a reality singing competition which searches for a champion among existing or established artistes rather than among new, unknown starlets as in other such singing competitions. The programme was co-launched with IKON Indonesia and IKON Philippines in late 2006 as an initiative to search for an artiste who can represent the country in the regional, ASEAN level. The verdict is determined by 70% of jury marks and 30% SMS., Ikon Asean is a regional music award designed to showcase and recognize talented artists from countries such as Malaysia, Indonesia and the Philippines. The First Ikon Asean was held on August 12, 2007 in Malaysia. , Malaysia is a federal constitutional monarchy located in Southeast Asia. It consists of thirteen states and three federal territories and has a total landmass of separated by the South China Sea into two similarly sized regions, Peninsular Malaysia and East Malaysia (Malaysian Borneo). Peninsular Malaysia shares a land and maritime border with Thailand and maritime borders with Singapore, Vietnam, and Indonesia. East Malaysia shares land and maritime borders with Brunei and Indonesia and a maritime border with the Philippines and Vietnam. The capital city is Kuala Lumpur, while Putrajaya is the seat of the federal government. With a population of over 30 million, Malaysia is the 44th most populous country. The southernmost point of continental Eurasia, Tanjung Piai, is in Malaysia. Located in the tropics, Malaysia is one of 17 megadiverse countries on earth, with large numbers of endemic species., Asian Idol is a reality singing competition, which featured winners of "Idol" competitions from six Southeast and South Asian countries consisting of India, Indonesia, Malaysia, Philippines, Singapore, and Vietnam. Part of the "Idol franchise", it originated from the reality program "Pop Idol" created by British entertainment executive Simon Fuller, which was first aired in 2001 in the United Kingdom. The first season was won by "Singapore Idol" Hady Mirza, who was awarded an all-expense-paid trip around the world on business class, after almost two million votes were cast., American Idol is an American singing competition television series created by Simon Fuller, produced by FremantleMedia North America and 19 Entertainment, and distributed by FremantleMedia North America. It began airing on Fox on June 11, 2002, and ended on April 7, 2016. It started off as an addition to the "Idols" format based on the British series "Pop Idol", and became one of the most successful shows in the history of American television. The concept of the series involves discovering recording stars from unsigned singing talents, with the winner determined by the viewers in America through telephones, Internet, and SMS text voting. Winners chosen by viewers in its fifteen seasons were Kelly Clarkson, Ruben Studdard, Fantasia Barrino, Carrie Underwood, Taylor Hicks, Jordin Sparks, David Cook, Kris Allen, Lee DeWyze, Scotty McCreery, Phillip Phillips, Candice Glover, Caleb Johnson, Nick Fradiani, and Trent Harmon., Subject: gemilang, Relation: record_label, Options: (A) 19 entertainment (B) india (C) philippines (D) pop (E) record (F) sony bmg

SOLUTION: sony bmg

PROBLEM: Context: Ego Trippin ' is the ninth studio album by American rapper Snoop Dogg ; it was released by Geffen Records on March 11 , 2008 . The album debuted at number 3 on the US Billboard 200 , selling 137,000 copies in its first week . Upon its release , the album received generally positive reviews from music critics ., Interscope Records is an American record company. A division of Interscope Geffen A&M Records, its parent company is the Universal Music Group, a subsidiary of Vivendi S.A., A record label or record company is a brand or trademark associated with the marketing of music recordings and music videos. Often, a record label is also a publishing company that manages such brands and trademarks, coordinates the production, manufacture, distribution, marketing, promotion, and enforcement of copyright for sound recordings and music videos; conducts talent scouting and development of new artists ("artists and repertoire" or "A&R"); and maintains contracts with recording artists and their managers. The term "record label" derives from the circular label in the center of a vinyl record which prominently displays the manufacturer's name, along with other information., Cordozar Calvin Broadus, Jr. (born October 20, 1971), known professionally as Snoop Dogg (formerly called Snoop Doggy Dogg and Snoop Lion), is an American rapper and actor from Long Beach, California. His music career began in 1992 when he was discovered by Dr. Dre of N.W.A, and as a result was prominently featured throughout Dr. Dre's solo debut album, "The Chronic" (1992). He has since sold over twenty-three million albums in the United States and thirty-five million albums worldwide., Geffen Records is an American major record label, owned by Universal Music Group, which operates as one third of the Interscope Geffen A&M Records label. Today, it is headquartered in the city of New York and is headed by Gee Roberson, who reports to John Janick, CEO of Interscope Records., Andre Romelle Young (born February 18, 1965), better known by his stage name Dr. Dre, is an American rapper, record producer, and entrepreneur. He is the founder and current CEO of Aftermath Entertainment and Beats Electronics. Dre was previously the co-owner of, and an artist on, Death Row Records. He has produced albums for and overseen the careers of many rappers, including 2Pac, The D.O.C., Snoop Dogg, Eminem, Xzibit, Knoc-turn'al, 50 Cent, The Game and Kendrick Lamar. He is credited as a key figure in the popularization of West Coast G-funk, a style of rap music characterized as synthesizer-based with slow, heavy beats. In 2014, Dr. Dre was ranked as the second richest figure in the American hip hop scene by "Forbes" with a net worth of $550 million; he is at the top of the 2015 "Forbes" list, with an estimated pre-tax take of $620 million in 2014., The Chronic is the debut studio album by American hip hop recording artist Dr. Dre. It was released on December 15, 1992, by his own record label Death Row Records and distributed by Priority Records. Recording sessions for the album took place in June 1992 at Death Row Studios in Los Angeles and at Bernie Grundman Mastering in Hollywood. The album is named after a slang term for high-grade cannabis, and its cover is a homage to Zig-Zag rolling papers. It was Dr. Dre's first solo album after he had departed from hip hop group N.W.A and its label Ruthless Records over a financial dispute. On "The Chronic", he included both subtle and direct insults at Ruthless and its owner, former N.W.A member Eazy-E. Although a solo album, it features many appearances by Snoop Dogg, who used the album as a launch pad for his own solo career., Universal Music Group, Inc. (also known as Universal Music Group Recordings, Inc. and abbreviated as UMG) is an American-French global music corporation that is a subsidiary of the Paris-based French media conglomerate Vivendi. UMG's global corporate headquarters are in Santa Monica, California., N.W.A (an abbreviation for Niggaz Wit Attitudes) was an American hip hop group from Compton, California. They were among the earliest and most significant popularizers and controversial figures of the gangsta rap subgenre, and are widely considered one of the greatest and most influential groups in the history of hip hop music. Active from 1986 to 1991, the rap group endured controversy owing to their music's explicit lyrics, which many viewed as being disrespectful to women, as well as to its glorification of drugs and crime. The group was subsequently banned from many mainstream American radio stations. In spite of this, the group has sold over 10 million units in the United States alone. The group was also known for their deep hatred of the police system, which sparked much controversy over the years., Subject: ego trippin', Relation: genre, Options: (A) album (B) dr (C) entertainment (D) gangsta rap (E) hip hop (F) information (G) marketing (H) music (I) radio

SOLUTION: hip hop

PROBLEM: Context: Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros., In Algebraic number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in formula_1 (the set of integers). The set of all algebraic integers, , is closed under addition and multiplication and therefore is a commutative subring of the complex numbers. The ring is the integral closure of regular integers formula_1 in complex numbers., Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ordinary integers formula_1, and "p"-adic integers., Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects 
meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics)., An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and 2048 are integers, while 9.75, , and  are not., 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., Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of "balance" and/or "symmetry". These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in Sudoku grids., Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets "S" indexed by the natural numbers, enumerative combinatorics seeks to describe a "counting function" which counts the number of objects in "S" for each "n". Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description. The twelvefold way provides a unified framework for counting permutations, combinations and partitions., In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of noncommutative rings where multiplication is not or is not required to be commutative., In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions., In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects. In many such problems, exhaustive search is not feasible. It operates on the domain of those optimization problems, in which the set of feasible solutions is discrete or can be reduced to discrete, and in which the goal is to find the best solution. Some common problems involving combinatorial optimization are the travelling salesman problem ("TSP") and the minimum spanning tree problem ("MST")., Algebra (from Arabic ""al-jabr"" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians., Combinatorial commutative algebra is a relatively new , rapidly developing mathematical discipline . As the name implies , it lies at the intersection of two more established fields , commutative algebra and combinatorics , and frequently uses methods of one to address problems arising in the other . Less obviously , polyhedral geometry plays a significant role . One of the milestones in the development of the subject was Richard Stanley 's 1975 proof of the Upper Bound Conjecture for simplicial spheres , which was based on earlier work of Melvin Hochster and Gerald Reisner . While the problem can be formulated purely in geometric terms , the methods of the proof drew on commutative algebra techniques . A signature theorem in combinatorial commutative algebra is the characterization of h - vectors of simplicial polytopes conjectured in 1970 by Peter McMullen . Known as the g - theorem , it was proved in 1979 by Stanley ( necessity of the conditions , algebraic argument ) and by Lou Billera and Carl W. Lee ( sufficiency , combinatorial and geometric construction ) . A major open question is the extension of this characterization from simplicial polytopes to simplicial spheres , the g - conjecture ., In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Polynomial rings have influenced much of mathematics, from the Hilbert basis theorem, to the construction of splitting fields, and to the understanding of a linear operator. Many important conjectures involving polynomial rings, such as Serre's problem, have influenced the study of other rings, and have influenced even the definition of other rings, such as group rings and rings of formal power series., Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra., Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory, like the existence of solutions to Diophantine equations., Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects (numbers, graphs, vectors, sets, etc.) can be, if it has to satisfy certain restrictions., Subject: combinatorial commutative algebra, Relation: instance_of, Options: (A) 1 (B) algebra (C) algebraic number (D) area (E) area of mathematics (F) behavior (G) branch (H) change (I) collection (J) complex number (K) computer (L) construction (M) description (N) design (O) economics (P) equation (Q) field (R) framework (S) function (T) group (U) integer (V) mathematics (W) medicine (X) notion (Y) number (Z) object ([) operation (\) operator (]) part (^) problem (_) quantity (`) range (a) rank (b) ring (c) science (d) set (e) size (f) space (g) study (h) theorem (i) theoretical computer science (j) theory (k) thread (l) two (m) understanding (n) vector

SOLUTION:
area of mathematics