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ntsh For each of the following relations on the integers Z, say whether is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/~. a.~y if and only if x > 0 and y > 0. b. xy if and only if |x| = |y|. c. xy if and only if x - y = 2.

ntsh For each of the following relations on the integers Z, say whether is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/~. a.~y if and only if x > 0 and y > 0. b. xy if and only if |x| = |y|. c. xy if and only if x - y = 2.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 15E: Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in...
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dong anong tuoitittan oldin bad-tiert odt not mold 1 = 1 101 bus 0 => odiorg mel 7 10 diod gut Preller of Z, say whether intsh For each of the following relations on the integers is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/~. a.~y if and only if x > 0 and y > 0. b. xy if and only if |x| = |y|. c. x~y if and only if x - y = 2.
Transcribed Image Text:dong anong tuoitittan oldin bad-tiert odt not mold 1 = 1 101 bus 0 => odiorg mel 7 10 diod gut Preller of Z, say whether intsh For each of the following relations on the integers is an equivalence relation; explain your answer. If is an equivalence relation, give an explicit description of the set of equivalence classes Z/~. a.~y if and only if x > 0 and y > 0. b. xy if and only if |x| = |y|. c. x~y if and only if x - y = 2.
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