Math 311W: Discrete Math Homework 6, due on Monday, Feb. 27 1. Let A = {{1}, 2, 3} and B = {, 1, {2}, 3}. Let P (A) be the power set of A, i.e., the set of all subsets of A. a) Find A B. b) Find P (A) \\ B. c) Find A (A B). d) Find a bijection f from A to B \\ A. Present it in the 2-row form. e) Find a function g from {0, 1} to B \\ A such that f 1 (g(x)) = x + 2 for x {0, 1}. Present it in the 2-row form. f) Does there exist a surjection from A (A B) to P (A) \\ B? Why? 2. Let f : X Y be a function and let A and B be subsets of X. We use the notation f (A) to denote the image of A under f , that is, f (A) = {f (x) : x A}. a) Show that f (A B) = f (A) f (B) (hint: to show \"=\