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 notcountable. True.(b) The number of functions from a set with 8 elements to a setwith 15 elements is C(15,8). False.(c) The coeffient of x3y5in the expansion of (x + y)8is thenumber of 3-permutations of an 8 element set. False.(d) There is a one-to-one correspondence between the realnumbers in the interval (-200,200) and the real numbers in theinterval (0,1). True.(e) The total number of ways to assign truth values to fivetrue-false problems by using the lettersTandFis given by thesum below. False.5C(5,k)k=16. (10 pts.)What is the minimum number of students required inyour Discrete Mathematics class to be sure that at least 4 havebirthdays occurring in the same month this year? Explain. Fromthe generalized pigeonhole principle, we need to find thesmallest positive integer N so that N/12 = 4. Thus,N = (3*12) + 1 = 37 will do.7. (10 pts.)The following proposition represents an invalidargument form:[q∧(p→q)]→p.(a) What is the name of the popular fallacy given by theproposition above? This is the infamous fallacy of affirming theconclusion. [Some logic texts call this the fallacy of affirming
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