Equivalence class and equivalence relation, Mathematics

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1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y).

(a) Prove that R is an equivalence relation on Z.

(b) If for every x ? Z, the equivalence class of x, [x], contains exactly one element, what can be said about the function f?

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