Let X be a set. Let P be a set of subsets of X such that: • Ø & P; the union of all sets A € Pis X. Note that these are clauses (a) and (c) of the definition of a partition (Definition 1.5). Now define a relation R on the set X by R={(x, y):x EA and ye A for some A € P}, as in Theorem 1.7(b). Which of the following is true? Select one: a. R must be reflexive and transitive but might not be symmetric. b. R must be reflexive and symmetric but might not be transitive. R must ho.cum
Let X be a set. Let P be a set of subsets of X such that: • Ø & P; the union of all sets A € Pis X. Note that these are clauses (a) and (c) of the definition of a partition (Definition 1.5). Now define a relation R on the set X by R={(x, y):x EA and ye A for some A € P}, as in Theorem 1.7(b). Which of the following is true? Select one: a. R must be reflexive and transitive but might not be symmetric. b. R must be reflexive and symmetric but might not be transitive. R must ho.cum
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...
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