Suppose that f : A → B and suppose that C ⊆ A and D ⊆ B.
(a) Prove or give a counterexample: f(C) ⊆ D iff C ⊆ f–1(D).
(b) What condition on f will ensure that f(C) = D iff C = f–1 (D)? Prove your answer.
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