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: The scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry is commonly based on empirical or measurable evidence subject to specific principles of reasoning. The Oxford Dictionaries Online define the scientific method as "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses". Experiments need to be designed to test hypotheses. The most important part of the scientific method is the experiment., The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism., Education is the process of facilitating learning, or the acquisition of knowledge, skills, values, beliefs, and habits. Educational methods include storytelling, discussion, teaching, training, and directed research. Education frequently takes place under the guidance of educators, but learners may also educate themselves. Education can take place in formal or informal settings and any experience that has a formative effect on the way one thinks, feels, or acts may be considered educational. The methodology of teaching is called pedagogy., A planetary nebula, often abbreviated as PN or plural PNe, is a kind of emission nebula consisting of an expanding, glowing shell of ionized gas ejected from old red giant stars late in their lives. The word "nebula" is Latin for mist or cloud, and the term "planetary nebula" is a misnomer that originated in the 1780s with astronomer William Herschel because when viewed through his telescope, these objects resemble the rounded shapes of planets. Herschel's name for these objects was popularly adopted and has not been changed. They are a relatively short-lived phenomenon, lasting a few tens of thousands of years, compared to a typical stellar lifetime of several billion years., Human science is the study and interpretation of the experiences, activities, constructs, and artifacts associated with human beings. The study of the human sciences attempts to expand and enlighten the human being's knowledge of their existence, its interrelationship with other species and systems, and the development of artifacts to perpetuate the human expression and thought. It is the study of human phenomena. The study of the human experience is historical and current in nature. It requires the evaluation and interpretation of the historic human experience and the analysis of current human activity to gain an understanding of human phenomena and to project the outlines of human evolution. Human science is the objective, informed critique of human existence and how it relates to reality., An emission nebula is a nebula formed of ionized gases that emit light of various colors. The most common source of ionization is high-energy photons emitted from a nearby hot star. Among the several different types of emission nebulae are H II regions, in which star formation is taking place and young, massive stars are the source of the ionizing photons; and planetary nebulae, in which a dying star has thrown off its outer layers, with the exposed hot core then ionizing them., Pedagogy is the discipline that deals with the theory and practice of education; it thus concerns the study of how best to teach. Spanning a broad range of practice, its aims range from furthering liberal education (the general development of human potential) to the narrower specifics of vocational education (the imparting and acquisition of specific skills)., Social science is a major category of academic disciplines, concerned with society and the relationships among individuals within a society. It in turn has many branches, each of which is considered a "social science". The main social sciences include economics, political science, human geography, demography, and sociology. In a wider sense, social science also includes some fields in the humanities such as anthropology, archaeology, jurisprudence, history, and linguistics. The term is also sometimes used to refer specifically to the field of sociology, the original 'science of society', established in the 19th century. A more detailed list of sub-disciplines within the social sciences can be found at Outline of social science., Harvard University is a private Ivy League research university in Cambridge, Massachusetts, established in 1636, whose history, influence, and wealth have made it one of the world's most prestigious universities., Science education is the field concerned with sharing science content and process with individuals not traditionally considered part of the scientific community. The learners may be children, college students, or adults within the general public; the field of science education includes work in science content, science process (the scientific method), some social science, and some teaching pedagogy. The standards for science education provide expectations for the development of understanding for students through the entire course of their K-12 education and beyond. The traditional subjects included in the standards are physical, life, earth, space, and human sciences., Eric J. Chaisson is an American astrophysicist best known for his research , teaching , and writing on the interdisciplinary science of cosmic evolution , a large public - domain web site for which can be accessed here . ( Closely related subjects include epic of evolution , big history , and astrobiology ) . He is also noted for his telescopic observations of interstellar clouds and emission nebulae of the Milky Way Galaxy , his empirical attempt to unify complexity science utilizing the technical concept of energy rate density , and his global leadership in improving science education nationally and internationally . He conducts research at the Harvard - Smithsonian Center for Astrophysics and teaches natural science at Harvard University ., A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking. , Subject: eric chaisson, Relation: occupation, Options: (A) academic (B) astronomer (C) faculty (D) jurisprudence (E) major (F) pedagogy (G) research (H) science

SOLUTION: astronomer

PROBLEM: Context: Florida (Spanish for "land of flowers") is a state located in the southeastern region of the United States. It is bordered to the west by the Gulf of Mexico, to the north by Alabama and Georgia, to the east by the Atlantic Ocean, and to the south by the Straits of Florida and Cuba. Florida is the 22nd most extensive, the 3rd most populous, and the 8th most densely populated of the U.S. states. Jacksonville is the most populous municipality in the state and is the largest city by area in the contiguous United States. The Miami metropolitan area is Florida's most populous urban area. The city of Tallahassee is the state capital., Orange Crush is Tim Dorsey 's third novel , and the first not to star Serge A. Storms as the main character . It is a frequently dark spoof of the politics of Florida and the United States ' involvement in the Balkans ., Bulgaria (tr. '), officially the Republic of Bulgaria (tr. '), is a country in southeastern Europe. It is bordered by Romania to the north, Serbia and Macedonia to the west, Greece and Turkey to the south, and the Black Sea to the east. With a territory of , Bulgaria is Europe's 16th-largest country., The Black Sea is a body of water between Eastern Europe and Western Asia, bounded by Bulgaria, Georgia, Romania, Russia, Turkey, and Ukraine. It is supplied by a number of major rivers, such as the Danube, Dnieper, Rioni, Southern Bug, and Dniester. The Black Sea has an area of (not including the Sea of Azov), a maximum depth of , and a volume of . It is constrained by the Pontic Mountains to the south and by the Caucasus Mountains to the east, and features a wide shelf to the northwest. The longest east-west extent is about ., Serbia, officially the Republic of Serbia, is a sovereign state situated at the crossroads of Central and Southeast Europe, covering the southern part of the Pannonian Plain and the central Balkans. Relative to its small territory, it is a diverse country distinguished by a "transitional" character, situated along cultural, geographic, climatic and other boundaries. Serbia is landlocked and borders Hungary to the north; Romania and Bulgaria to the east; Macedonia to the south; and Croatia, Bosnia-Herzegovina, and Montenegro to the southwest; it also claims a border with Albania through the disputed territory of Kosovo. Serbia numbers around 7 million residents, and its capital, Belgrade, ranks among the largest cities in Southeast Europe., The contiguous United States consists of the 48 adjoining U.S. states plus Washington, D.C. (federal district), on the continent of North America. The term excludes the non-contiguous states of Alaska and Hawaii and all off-shore United States territories and possessions, which include American Samoa, Guam, the Northern Mariana Islands, Puerto Rico, and the U.S. Virgin Islands., John Dann MacDonald (July 24, 1916  December 28, 1986) was an American writer of novels and short stories, known for his thrillers., Cuba, officially the Republic of Cuba, is a country comprising the island of Cuba as well as Isla de la Juventud and several minor archipelagos. Cuba is located in the northern Caribbean where the Caribbean Sea, the Gulf of Mexico, and the Atlantic Ocean meet. It is south of both the U.S. state of Florida and the Bahamas, west of Haiti, and north of Jamaica. Havana is the largest city and capital; other major cities include Santiago de Cuba and Camagüey. Cuba is the largest island in the Caribbean, with an area of , and the second-most populous after Hispaniola, with over 11 million inhabitants., The Straits of Florida, Florida Straits, or Florida Strait is a strait located south-southeast of the North American mainland, generally accepted to be between the Gulf of Mexico and the Atlantic Ocean, and between the Florida Keys (U.S.) and Cuba. It is 150 km (93 mi) wide at the narrowest point between Key West and the Cuban shore, and has been sounded to a depth of 6,000 feet. The strait carries the Florida Current, the beginning of the Gulf Stream, from the Gulf of Mexico., The Balkan Peninsula, or the Balkans, is a peninsula and a cultural area in Eastern and Southeastern Europe with various and disputed borders. The region takes its name from the Balkan Mountains that stretch from the Serbia-Bulgaria border to the Black Sea., The Atlantic Ocean is the second largest of the world's oceans with a total area of about . It covers approximately 20 percent of the Earth's surface and about 29 percent of its water surface area. It separates the "Old World" from the "New World"., Florida Roadkill is the first book in the unnamed series of books by Tim Dorsey which were centered on his character Serge Storms. It was published in 1999 by William Morrow and Company, an imprint of HarperCollins., The euro (sign: €; code: EUR) is the official currency of the eurozone, which consists of 19 of the member states of the European Union: Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, and Spain. The currency is also officially used by the institutions of the European Union and four other European countries, as well as unilaterally by two others, and is consequently used daily by some 337 million Europeans . Outside of Europe, a number of overseas territories of EU members also use the euro as their currency., Europe is a continent that comprises the westernmost part of Eurasia. Europe is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, and the Mediterranean Sea to the south. To the east and southeast, Europe is generally considered as separated from Asia by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways of the Turkish Straits. Yet the non-oceanic borders of Europea concept dating back to classical antiquityare arbitrary. The primarily physiographic term "continent" as applied to Europe also incorporates cultural and political elements whose discontinuities are not always reflected by the continent's current overland boundaries., Tim Dorsey (born January 25, 1961) is an American novelist, frequently compared to Dave Barry and Carl Hiaasen (who both had cameo appearances in his first book, "Florida Roadkill"). Dorsey's books are crime capers in the Florida style pioneered by John D. MacDonald., Subject: orange crush , Relation: publisher, Options: (A) europe (B) france (C) germany (D) macdonald (E) north america (F) slovenia (G) the atlantic (H) turkey (I) william morrow and company

SOLUTION:
william morrow and company