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Suppose f : X → S and F ⊆ P(S). Show, f −1 (∪A∈F A) =...

Suppose f : X → S and F ⊆ P(S). Show, f −1 (∪A∈F A) = ∪A∈F f −1 (A) f −1 (∩A∈F A) = ∩A∈F f −1 (A)

Show, if A, B ⊆ X, then f(A ∩ B) ⊆ f(A) ∩ f(B). Give an example, if possible, where strict inclusion holds.

Show, if C ⊆ X, then f −1 (f(C)) ⊇ C. Give an example, if possible, where strict inclusion holds.

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