7. Decide for each of the following relations whether or not it is an equivalence relation. Give full reasons. If it is an equivalence relation, give the equivalence classes. (a) Let a, b € Z. Define aRb if and only if - € z (b) Let a and b be integers. Define aRb if and only if 3|(a – b) (In other words R is the congruence modulo 3 relation

7. Decide for each of the following relations whether or not it is an equivalence relation. Give full reasons. If it is an equivalence relation, give the equivalence classes. (a) Let a, b € Z. Define aRb if and only if - € z (b) Let a and b be integers. Define aRb if and only if 3|(a – b) (In other words R is the congruence modulo 3 relation

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...

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