(Properties of the inverse image of functions and continuity) Let f: C C be any function, show that for any A, B C 1. f(AUB) = f(A)uf-(B) 2. f(An B) = f'(A) nf-(B) 3. f(A) = f(B) if A = B 4. f(AB) = f(A) f(B) where f(D) = {z C: f(z) e D} and Z\D = {z Z: z D}