or "false".Be sure to write out the entire word.(a) The set of all subsets of the natural numbers is countable.False.(b) The number of one-to-one functions from a set with 8elements to a set with 15 elements is P(15,8). True.(c) The coeffient of x3y5in the expansion of (x + y)8is thenumber of 3 element subsets of an 8 element set. True.(d) There is a one-to-one correspondence between the naturalnumbers and the real numbers in the interval (0,1). False.(e) The total number of ways to assign truth values to fivetrue-false problems by using the lettersTandFis given by thesum below. True.5C(5,k)k=06. (10 pts.)What is the minimum number of students required inyour Discrete Mathematics class to be sure that at least 4 havebirthdays occurring on the same day of the week this year?Explain. From the generalized pigeonhole principle, we need tofind the smallest positive integer N so that N/7 = 4. Thus,N = (3*7) + 1 = 22 will do.7. (10 pts.)(10 pts.) The following proposition represents aninvalid argument form:[¬p∧(p→q)]→¬q.(a) What is the name of the popular fallacy given by theproposition above? This is the infamous fallacy of denying thehypothesis. [Some logic texts call this the fallacy of denyingthe antecedent.](b) Why is reasoning using this argument form deemed invalid?
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