(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 thatN/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?
This is the end of the preview.
access the rest of the document.