Question: Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Let R be the relation on

Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Let R be the relation on F defined by For all f, g E F, f Rg if and only if there exist r, y E A so that f (I) = g(y). (a) Prove that for all f E F, fRIA. (b) Is R reflexive? Prove your answer. (c) Is R symmetric? Prove your answer. (d) Is R transitive? Prove your answer. (e) Is R an equivalence relation on F? Explain

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