Exercise 11 Sets and maps 1. Determine which of the following is a map: (a) : N-+ N, defined by p ( 20 ) = 1 1, 2 x = 1, 2 + 2 a > 1. (b) 2 : R -+ R, defined by (x ) = 12+2 2 = 1, x # 1. (c) w : C-+ C defined by: w ( 20 ) = 3 5 x = 1, 2, 3 * + 2 x * 1, 2, 3. 2. Which of the maps in Problem 1. are 1-1, onto? 3. For y and w in Problem 1. evaluate you and wow. 4. If S and T are finite sets show that |S x TI = ISIITI. 5. If S is a finite set show that |P(S) | = 2151. 6. Prove that: (a) for any set S, ids is a bijection. (b) The composite of onto set maps y and y is onto. (c) The composite of 1-1 set maps is 1-1