1. 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
2. Suppose that f : A → B and let C be a subset of A.
(a) Prove or give a counterexample: f ( A\C ) ⊆ f ( A)\ f (C ).
(b) Prove or give a counterexample: f ( A)\ f (C ) ⊆ f ( A\C ).
(c) What condition on f will ensure that f ( A\C ) = f ( A)\ f (C )? Prove your answer.
(d) What condition on f will ensure that f ( A\C ) = B \ f (C )? Prove your answer.
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