Inverse image. For the following functions f: X Y and SCY deter- mine f-(S): (a) f: R2R given by f(x, y) = x - y and S = [0, 1]. (b) X a finite set and f: 2x x 2X 2X given by f(A, B) = An B and S = {X}. (c) f: Q Q2 given by f(x, y) = (2x - y, -x + y) and S = (2, 3). 3. Prove that for any subset SC X of a set X we have 15({1}) = S. What is 1({0})?