Question

# Suppose that f : X → Y is a function, and that A ⊂ X and B ⊂ X.

a) Prove that f(A ∩ B) ⊂ f(A) ∩

f(B).

b) Prove that f(A ∩ B) = f(A) ∩ f(B) given that f is an injective map.

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