5. (10 points) Let f be a function from A to B, and let C be a subset of B. The inverse image of C is f 1 (C) = {a A | f(a) C}. Give a a proof of the following theorem: for any subsets S and T of B, f 1 (S T) = f 1 (S) f 1 (T) (You should give an informal proof, meaning a direct proof, proof by contraposition, proof by contradiction, etc.