3. If A and B are sets and f: A B, then for any subset S of A we define f(S) = {be B:b= f(a) for some a e S} . Similarly, for any subset T of B we define the pre-image of T as f-1(T) = {a e A: f(a) T} . Note that f-1(T) is well defined even if f does not have an inverse ! For each of the following state whether it is True or False. If True then give a proof. If False then give a counterexample: (a) f( SS2) = f(Si) u f(S2) (b) f(Sin S2) = f(Si)n f(S2) (c) f-1(TT) = f-1(T) uf-1(72) (d) f-1(Tin Ty) = f-1(T) nf-1(T2)