Let f: A B be a function. Let X be a subset of A. (a) Verify that X ≤ f−¹(ƒ(X)). (b) Give an example of sets X CA and B, and a function f : A → B such that f−¹(f(X)) £ X. (c) Prove that if f is injective then X = f−¹(ƒ(X)).

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