NOTE: THIS IS CHAPTER 2 - FUNCTIONS- IN "DISCRETE MATHEMATICS" (AKA DISCRETE STRUCTURE) COURSE FOR COMPUTER SCIENCE**

2.3.4: Only a,c,e,g

2.4.2: Only a,c,e,g

EXERCISE 2.3.4: Properties of functions on strings and power sets. For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one-to- one, give an example showing why (a) f: {0, 1)4(0, 1)3. The output of f is obtained by taking the input string and dropping the first bit. For example f(1011) = 011 . f: (0. 1},{0, 1}3. The output of f is obtained by taking the input string and replacing the first bit by 1, regardless of whether the first bit is a 0 or 1 . For example, (001) = 101 and f(110) = 1 10. (c) f (0, 1)3 0, 1)3. The output of f is obtained by taking the input string and reversing the bits. For example f(011) 110 f: (0, 1}3(0, 1}. The output of f is obtained by taking the input string and adding an extra copy of the first bit to the end of the string. For example, f(100) -1001 Let A be defined to be the set(1, 2, 3, 4, 5, 6, 7, 8} f: P(A) {0, 1, 2, 3, 4, 5, 6, 7, 8} For Xc A, f(X)-lxl Recall that for a finite set A, P(A) denotes the power set of A which is the set of all subsets of A Let A be defined to be the set {1, 2, 3, 4, 5,6, 7, 8). f: P(A) PA) For Xc A, f(X) = X. Recall that for a finite set A, P(A) denotes the power set of A which is the set of all subsets of A. (a) Let A be defined to be the set (1,2,3,4,5,6,7,8) and let B-(1).f PA P(A) denotes the power set of A which is the set of all subsets of A. P(A).ForXSAfx)-x-B. Recall that for a finite set A