(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 thatN/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 affirmingthe consequent.](b)Why is reasoning using this argument form deemed invalid?
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