We are given a function f : X Y a) Show that for all sets G, H C Y we have i) f- (GUH) = (G) u (H), and ii) (G ^ H) = -(G)n f(H). b) Show that for A, B C X, we have i) f(AUB) = f(A) U f(B) and ii) f(An B) f(A)n f(B). c) Construct an example of a function f such that the inclusion in b.ii) is proper(strict) for some choice of sets A and B. d) Show that f : X Y is injective if and only if for all A, B C X, we have f(An B) = f(A)n f(B).