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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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The hole set of irrational and rational numbers is the set of real numbers and is representing by R. Thus, the real numbers can also be describe in terms of position of a point on
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