A the set of all subsets of the natural numbers is

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(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=3 7 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 the consequent.] (b) Why is reasoning using this argument form deemed invalid?
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