Let R be the relation on the all integers given by xRy iff x- y = 2k for someinteger k. (1) Prove that the relation is an equivalence relation. (2) Find the equivalenceclasses [0] and [1]

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Answered: Let R be the relation on the all…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Let R be the relation on the all integers given by xRy iff x- y 2k for some integer k. (1) Prove that the relation is an equivalence relation. (2) Find the equivalence classes [0] and [1]