# Label each of the following assertions with true or

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Label each of the following assertions with "true" or "false". Be sure to write out the entire word. (a) The set of all subsets of the natural numbers is not countable. True. (b) The number of functions from a set with 8 elements to a set with 15 elements is C(15,8). False. (c) The coeffient of x 3 y 5 in the expansion of (x + y) 8 is the number of 3-permutations of an 8 element set. False. (d) There is a one-to-one correspondence between the real numbers in the interval (-200,200) and the real numbers in the interval (0,1). True. (e) The total number of ways to assign truth values to five true-false problems by using the letters T and F is given by the sum below. False. 5 C(5,k) k=1 6. (10 pts.) What is the minimum number of students required in your Discrete Mathematics class to be sure that at least 4 have birthdays occurring in the same month this year? Explain. From the generalized pigeonhole principle, we need to find the smallest positive integer N so that N/12 = 4. Thus, N = (3*12) + 1 = 37 will do. 7. (10 pts.) The following proposition represents an invalid argument form: [q (p q)] p. (a) What is the name of the popular fallacy given by the proposition above? This is the infamous fallacy of affirming the conclusion. [Some logic texts call this the fallacy of affirming
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