Question

Consider Theorem 3.25: Theorem 3.25. Let f : A → B, let S, T ⊆ A,...

Consider Theorem 3.25:

Theorem 3.25. Let f : A → B, let S, T ⊆ A, and let V , W ⊆ B.

1. f(S ∪T) = f(S)∪f(T)

2. f(S ∩T) ⊆ f(S)∩f(T)

3. f-1(V ∪W) = f-1(V )∪f−1(W)

4. f-1(V ∩W) = f-1(V )∩f−1(W)

(a) Prove statement (2).

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

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

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