the following questions.
(a) How many ways are there to choose committees consisting of
four members of the club?
(b) How many ways are there to choose a president, vice
president, secretary, and treasurer of the club?
(c) How many ways are there to choose committees consisting of
four people if exactly three of the four must be female?
(d) How many ways are there to choose committees consisting of
four people if none of them can be female?
(e) How many ways are there to choose committees consisting of
four people if at least one must be female.
8. (5 pts.)
(a) The following proposition represents an
invalid argument form:
[¬p
∧
(p
→
q)]
→
¬q.
What is the name of the popular fallacy given by the proposition
above?
(b) The following proposition represents an invalid argument
form:
[q
∧
(p
→
q)]
→
p.
What is the name of the popular fallacy given by the proposition
above?
(c) Why is reasoning using either of the argument forms found in
(a) or (b) deemed invalid?
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MAD2104/Final Exam Page 4 of 8
9. (5 pts.)
Label each of the following assertions with "true"
or "false".
Be sure to write out the entire word.
(a) The set of all subsets of the natural numbers is countable.
(b) The number of functions from a set with 8 elements to a set
with 15 elements is P(15,8).
(c) The coeffient of x
4
y
5
in the expansion of (x + y)
9
is the
number of 5 element subsets of an 9 element set.
(d) There is a onetoone correspondence between the natural
numbers and the rational numbers.
(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.
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 Spring '08
 STAFF
 Logic, pts, Natural number, MAD2104/Final Exam

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