1. Let Z be the set of integers and let m be a fixed positive integer. Define the relation by xy if and only if m divides x - 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 Z6.

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