(a)
The set of all subsets of the natural numbers is countable.
False.
(b)
The number of onetoone functions from a set with 8
elements to a set with 15 elements is P(15,8).
True.
(c)
The coeffient of x
3
y
5
in the expansion of (x + y)
8
is the
number of 3 element subsets of an 8 element set.
True.
(d)
There is a onetoone correspondence between the natural
numbers and the real numbers in the interval (0,1).
False.
(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. True.
5
C(5,k)
k=0
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 on the same day of the week this year?
Explain. From the generalized pigeonhole principle, we need to
find the smallest positive integer N so that
N/7
= 4. Thus,
N = (3*7)+1=2
2 will do.
7. (10 pts.)
(10 pts.) The following proposition represents an
invalid argument form:
[¬p
∧
(p
→
q)]
→
¬q.
(a)
What is the name of the popular fallacy given by the
proposition above?
This is the infamous fallacy of denying the
hypothesis. [Some logic texts call this the fallacy of denying
the antecedent.]
(b)
Why is reasoning using this argument form deemed invalid?
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 Spring '08
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 Logic, Mathematical Induction, pts, Natural number, induction step, Recursive definition

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