Problem 5 Let A and B be sets, let R and S be relations on A and B, respectively, and let f : A →B be a function. The function f is relation preserving if xRy if and only if f (x)Sf (y), for all x, y ∈A. 1. Suppose that f is bijective & relation preserving. Prove that f^(−1) is relation preserving. 2. Suppose that f is surjective & relation preserving. Prove that R is reflexive, symmetric or transitive if and only if S is reflexive, symmetric or transitive, respectively.

Q: Do question 2 only

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

Q: Do question 1 only

A: For any query with the solution, please ask in the comment box.

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

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