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Let f : A → B, and let V ⊆ B. (a) Prove that V ⊇...

Let f : A → B, and let V ⊆ B.

(a) Prove that V ⊇ f(f−1(V )).

(b) Give an explicit example where the two sides are not equal.

(c) Prove that if f is onto then the two sides must be equal.

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