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: Latin (Latin: ) is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets., In mathematics, a rational number is any number that can be expressed as the quotient or fraction "p"/"q" of two integers, a numerator "p" and a non-zero denominator "q". Since "q" may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", is usually denoted by a boldface Q (or blackboard bold formula_1, Unicode ); it was thus denoted in 1895 by Giuseppe Peano after "quoziente", Italian for "quotient"., In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization., A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests "prove" that a number is prime, while others like MillerRabin prove that a number is composite. Therefore, the latter might be called "compositeness tests" instead of primality tests., Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers)., A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3., Paul Leyland is a British number theorist who has studied integer factorization and primality testing., Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts. This was a recognizable category of mathematical activity from the 19th century onwards, at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, and so on., In number theory , a Leyland number is a number of the form x ^ y + y ^ x where x and y are integers greater than 1 . They are named after the mathematician Paul Leyland . The first few Leyland numbers are 8 , 17 , 32 , 54 , 57 , 100 , 145 , 177 , 320 , 368 , 512 , 593 , 945 , 1124 ( sequence A076980 in OEIS ) . The requirement that x and y both be greater than 1 is important , since without it every positive integer would be a Leyland number of the form x1 + 1x . Also , because of the commutative property of addition , the condition x  y is usually added to avoid double - covering the set of Leyland numbers ( so we have 1 < y  x ) . The first prime Leyland numbers are 17 , 593 , 32993 , 2097593 , 8589935681 , 59604644783353249 , 523347633027360537213687137 , 43143988327398957279342419750374600193 ( A094133 ) corresponding to 32 +23 , 92 +29 , 152 +215 , 212 +221 , 332 +233 , 245 +524 , 563 +356 , 3215 +1532 . One can also fix the value of y and consider the sequence of x values that gives Leyland primes , for example x2 + 2x is prime for x = 3 , 9 , 15 , 21 , 33 , 2007 , 2127 , 3759 , ... ( A064539 ) . By November 2012 , the largest Leyland number that had been proven to be prime was 51226753 + 67535122 with 25050 digits . From January 2011 to April 2011 , it was the largest prime whose primality was proved by elliptic curve primality proving . In December 2012 , this was improved by proving the primality of the two numbers 311063 + 633110 ( 5596 digits ) and 86562929 + 29298656 ( 30008 digits ) , the latter of which surpassed the previous record . There are many larger known probable primes such as 3147389 + 9314738 , but it is hard to prove primality of large Leyland numbers . Paul Leyland writes on his website : `` More recently still , it was realized that numbers of this form are ideal test cases for general purpose primality proving programs . They have a simple algebraic description but no obvious cyclotomic properties which special purpose algorithms can exploit . '' There is a project called XYYXF to factor composite Leyland numbers ., 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., 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., Subject: leyland number, Relation: subclass_of, Options: (A) algorithm (B) blackboard (C) branch (D) category (E) complex number (F) decomposition (G) economics (H) engineering (I) integer (J) language (K) latin (L) mathematics (M) meeting (N) natural (O) natural number (P) number (Q) out (R) polynomial (S) problem (T) process (U) rational number (V) ring (W) set (X) test (Y) theorem (Z) theory ([) thought (\) time

SOLUTION: natural number

PROBLEM: Context: Doong Spank is the title of the fourth studio album by Bahamas - based musical group Baha Men . It was their second studio album on a major label ., "Who Let the Dogs Out?" is a song performed by Bahamian group Baha Men, released as a single on 26 July 2000. Originally written by Anslem Douglas (titled "Doggie") for the Trinidad and Tobago Carnival season of 1998, it was covered by producer Jonathan King under the name Fat Jakk and his Pack of Pets. He brought the song to the attention of his friend Steve Greenberg, who then had the Baha Men cover the song. The song became the band's first hit in the United Kingdom and the United States, and it gained popularity after appearing in "" and its soundtrack album., Junkanoo is a street parade with music, dance, and costumes of Akan origin in many towns across the Bahamas every Boxing Day (December 26) and New Year's Day (January 1), the same as "Kakamotobi" or the Fancy Dress Festival. The largest Junkanoo parade happens in the capital New Providence. There are also Junkanoo parades in Miami in June and Key West in October, where local black American populations have their roots in The Bahamas. In addition to being a culture dance for the Garifuna people, this type of dancing is also performed in The Bahamas on Independence day and other historical holidays., Baha Men are a Bahamian band playing a modernized style of Bahamian music called junkanoo. They are best known for their 2000 hit single "Who Let the Dogs Out?"., Subject: doong spank, Relation: followed_by, Options: (A) 1 (B) 2000 (C) 26 (D) a (E) a single (F) a song (G) album (H) attention (I) best (J) carnival (K) covered (L) dance (M) dancing (N) december 26 (O) fancy (P) is (Q) king (R) kingdom (S) miami (T) music (U) new (V) october (W) on (X) originally (Y) parade (Z) providence ([) released (\) single (]) soundtrack (^) style (_) the band (`) this (a) united (b) who let the dogs out

SOLUTION: who let the dogs out

PROBLEM: Context: The Brady Kids is an animated television series , produced by Filmation in association with Paramount Television and seen on ABC from 1972 to 1973 . It was an animated spin - off based on ABC 's live action sitcom , The Brady Bunch and spun off another Filmation series , Mission : Magic ! , starring rock star Rick Springfield . The series is distributed by CBS Television Distribution ., Paramount Television is an American television production/distribution company that was active from 1967 until 2006 and revived in 2013. Most of this time it served as the television arm of the Paramount Pictures film studio. Its predecessor is Desilu Productions., Desilu Productions was an American television production company co-owned by husband and wife Desi Arnaz and Lucille Ball, best known for shows such as "I Love Lucy", "", and "The Untouchables". Until 1962, Desilu was the second-largest independent television production company in the U.S. behind MCA's Revue Productions until MCA bought Universal Pictures, and Desilu became and remained the number-one independent production company until being sold in 1967. Ball and Arnaz jointly owned the majority stake in Desilu from its inception until 1962, when Ball bought Arnaz out and ran the company by herself for several years. Ball had succeeded in making Desilu profitable again by 1967, when she sold her shares of Desilu to Gulf+Western / Paramount Studios for $17 million. After the sale, company officials renamed it Paramount Television., Filmation Associates was a production company that produced animation and live-action programming for television from 1963 to 1989. Located in Reseda, California, the animation studio was founded in 1962. Filmation's founders and principal producers were Lou Scheimer, Hal Sutherland and Norm Prescott., Norman "Norm" Prescott (January 31, 1927  July 2, 2005) was co-founder and executive producer at Filmation Associates, an animation studio he created with veteran animator Lou Scheimer. Born in the Dorchester neighborhood of Boston, his real name was Norman Pransky. His father Edward was a tailor and a shirt-maker., Subject: the brady kids, Relation: director, Options: (A) desi arnaz (B) hal sutherland (C) lou scheimer

SOLUTION:
hal sutherland

