Question: 1. Let f: A > B be a function. Let X be a subset of A. (a) Verify that X g f'1(f(X)). (b) Give an

1. Let f: A > B be a function. Let X be a subset of A. (a) Verify that X g f'1(f(X)). (b) Give an example of sets X g A and B, and a function f : A > B such that f1(f(X)) g X. (c) Prove that if f is injective then X = f'1(f(X)). 2. Let f : A > B be a function. Let X and Y be subsets of A. (a) Verify that f(X) f(Y) g f(X Y). (b) Give an example of sets X,Y g A and B, and a function f : A > B such that f(X Y) 9: f(X) f(Y)

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