(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 3permutations of an 8 element set. False.
(d)
There is a onetoone 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
truefalse 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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 Spring '08
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 Logic, Mathematical Induction, Natural number, induction step, Recursive definition

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