2 Let Z be the set of integers and let m be a fixed positive integer. Define the relation by y if and only if m divides a- y (equivalently ay is a multiple of m). This is called the relation congruence modulo m in Z. (a) Prove that this relation is an equivalence relation. (b) What are the distinct equivalence classes when m = 6? These are also known as the residue classes modulo 6 and the set of these residue classes is denoted by Ze.

2 Let Z be the set of integers and let m be a fixed positive integer. Define the relation by y if and only if m divides a- y (equivalently ay is a multiple of m). This is called the relation congruence modulo m in Z. (a) Prove that this relation is an equivalence relation. (b) What are the distinct equivalence classes when m = 6? These are also known as the residue classes modulo 6 and the set of these residue classes is denoted by Ze.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 8E: In Exercises 610, a relation R is defined on the set Z of all integers. In each case, prove that R...

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