Csci 2610, Fall 2008
Final Exam
2008.12.16
1
Name: _________________________________
Seat:_______________
The Final Exam has 14 questions worth a total of 100 points. Please make
certain you have all 8 pages. You will have 180 minutes to complete the exam.
You are allowed a twosided sheet of paper with notes. You may use a calculator.
Unless otherwise instructed, give all probabilities as decimals, percents, or
fractions (e.g., 0.0568, 12.3%, or 5/6).
1.
(5 points)
Show that
((p
r)
(q
r)) is logically equivalent to (p
q)
r.
2.
(5 points)
Let P(x,y) be the statement “x is a parent of y.” (Or “y is a child of x.”)
Let R(x,y) be the statement “x is related to y.” (This refers to a family relation).
The universe of discourse for both predicates is all people.
Using quantifiers, write the following propositions:
a)
Everyone has a parent.
b)
Any two people must be related if they are parent and child.
c)
Someone is a grandparent.
d)
A predicate Q(x,y) is
symmetric
iff
x
y(Q(x,y)
Q(y,x)). Which of the
above predicates is symmetric?
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Csci 2610, Fall 2008
Final Exam
2008.12.16
2
3.
(5 points)
Use a symbolic proof to derive
x(
P(x)
S(x)) from the premises
x(R(x)
Q(x)),
x(S(x)
R(x)), and
x(P(x)
Q(x)).
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 Fall '08
 smith
 Computer Science, Logic, 180 minutes, 12.3%, primeCounter

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