Question: Let f : A X be a function and let B be a subset of A. (a) Prove that B f 1 (f(B)). (b) Give

Let f : A X be a function and let B be a subset of A.

(a) Prove that B f 1 (f(B)).

(b) Give an example showing that the inclusion can be proper, that is, B 6= f 1 (f(B)).

(c) Determine whether equality must hold if we assume that f is injective; justify your answer with a proof or a counterexample.

(d) Determine whether equality must hold if we assume that f is surjective (not necessarily injective); justify your answer with a proof or a counterexample.

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