Discrete Structures
HW #4 —
§1.4: Nested Quantifiers
Last Update: 24 September 2010
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Each HW problem's solution should consist of:
All solutions must be handwritten.
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& "HW #4"
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 (3 points each; total = 21 points)
p. 59: 10 a–b, d, f–i
 This problem asks you to translate 7 English sentences
into the language of FOL
(using one, 2place predicate).
 (3 points each; total = 12 points)
p. 59: 12 a, d, f–g
 This problem asks you to translate 4 English sentences
into the language of FOL
(using one, 1place predicate and one,
2place predicate).
 (3 points each; total = 15 points)
p. 61: 28 a–e
 This problem gives you 5 FOL propositions whose
domain is R (the set of all real numbers),
and asks you to determine their truth values.
 If a universally quantified proposition is false,
give a counterexample!
 You may have to do a bit of elementary algebra;
if you need algebra hints,
send
me email.
 It may help if you translate the FOL into English.
 You will get partial credit only if you show all your work.
(And by now you should know what "only if" means :)
 (3 points each; total = 12 points)
p. 61: 32 a–d
 This problem gives you 4 FOL propositions,
and asks you to compute their negations in such a way
that all negation signs appear only in front of predicates.
Here's an example: As you learned in lecture
and read about in the text,
So, the negation of ∀xP(x) can be written in
either of those two ways.
But only the one on the righthand side of
the logicalequivalence sign has its negation sign in front of the
predicate.
 Hint for part (c): Do you remember what the negation
of a biconditional is?
Total points = 60
Tentative grading scheme:
A 5760
A 5456
B+ 5153
B 4750
B 4446
C+ 4143
C 3440
C 2733
D+ 2126
D 1120
F 010
DUE: AT THE BEGINNING OF LECTURE, FRI., OCT. 1 
Text copyright © 2010 by William J. Rapaport
(rapaport@buffalo.edu)
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http://www.cse.buffalo.edu/~rapaport/191/F10/hw04.html20100923