Let A = {1, 2, 3, 4, 5}. Let F be the set of all functions from A to A. Define a relation R on F as follows: For all f, g € F, ƒ Rg ⇒ for all i ¤ A, f(i) ≤ g(i). (a) Is R reflexive? symmetric? antisymmetric? transitive? Prove your answers. (b) Prove or disprove: There exists g E F so that for all f € F, f Rg. (c) Prove or disprove: For all f € F, there exists g E F so that fRg.

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