Section 1.3 10. Find four relations from {a, b} to {x, y} that are not functions from {a, b} to {x, y}. 15. Let X ={2,4,5}and Y = {1, 2, 4, 6}. Which of the following arrow diagrams determine functions from X to Y? 18. Let h be the constant function defined in Example 1.3.6. Find h(-12/5), h(0/1), and h(9/17). Section 2.1 11. In the following sentence, is the word or used in its inclusive or exclusive sense? A team wins the playoffs if it wins two games in a row or a total of three games. Determine whether the statement forms in 16,17, 18, 19, 20, 21, 22, 23, and 24 are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. 20.pAcandpVece 24. (pvg)V(pAr)and (pvg)Ar 31. Let s be a string of length 2 with characters from {0,1,2), and define statements a, b, c, and d as follows: a = "the first character of s is 0" b = "the first character of s is 1" c = "the second character of s is 1" d = "the second character of s is 2" Describe the set of all strings for which each of the following is true: a. (a V b) A (cv d) b. (~(avb))A (cvd) c. (~a) V (b) A (cv (~d) ) In 38 and 39, imagine that num_orders and num_instock are particular values, such as might occur during execution of a computer program. Write negations for the following statements. 39. (num_orders 300) or (50 5) Use Theorem 2.1.1 to verify the logical equivalences in 50, 51, 52, 53, and 54. Supply a reason for each step. 54. (PA (~(~PV q))) V (PA q) =P 5