27. Let A be a set and let f: A A be a function. For x, y E A, define x ~ y if f(x) = f(y). (a) Prove that ~ is an equivalence relation on A'. (b) For A =R and f(x) = [x], find the equivalence classes of 0, , and -.

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A: (a) For every m ∈ Z, 5 | (m2 −m2) = 0      Hence, m ~ m for all m ∈ Z      Hence, ~ is reflexive.

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A: We are allowed to do a maximum three sub parts as per bartleby guidelines

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Q: f(y). (a) Prove that is an (b) Find a bijection from A/~ to B. equivalence relation.

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