Proposition 8.59. Suppose that X, Y, W, Z, A, B are sets. Let f
: X → Y , W ⊆ X, Z ⊆ X, A ⊆ Y , and B ⊆ Y . Then the following are
true:
prove the following ?
(1) f(W ∩ Z) ⊆ f(W) ∩ f(Z).
(2) f(W ∪ Z) = f(W) ∪ f(Z).
(3) f−1(A ∩ B) ⊆ f−1(A) ∪ f−1(B)
4) f−1(A ∪ B) = f−1(A) ∪ f−1(B).
(5) X−f−1(A)⊆f−1(Y −A).
(6) W...