Let X = {0, 1, 2, . .., n - 1, , n} and Y = {-n, -n + 1,...,-2, -1,0}, where n is a positive integer. Define f : Pz( X ) x P2 (Y) - Pa(XUY)UP(XUY) by f(A, B) = AUB. Suppose that f(A, B) = f(C, D). This applies to all of the following parts. Helpful fact: XnY = {0} (the singleton). (a) Suppose that 0 E A. Prove that A = C. Hint: What form does the set A take? (b) Suppose that 0 @ A. Prove that A = C. (c) Prove that f is injective