CS 173: Discrete Structures, Fall 2011
Homework 2
This homework contains 5 problems worth a total of 47 points. It is due on Friday, Septem
ber 9th at 4pm. As usual, put your homework into the appropriate dropbox in the base
ment of Siebel.
1.
[9 points] Truth tables
(a) (3 points) Give the truth table corresponding to the following expression:
(
p
→
q
)
∧
r
Include a column for the intermediate result
(
p
→
q
)
.
(b) (2 points) Eager Eddy from down the hall claims that
(
p
→
q
)
∧
r
and
p
→
(
q
∧
r
)
are logically equivalent. Disprove his claim using a concrete counterexample.
That is, give
specific
values for
p
,
q
and
r
for which the two expressions produce
different values.
(c) (4 points) For which values of
p
,
q
, and
r
is the following logical expression true?
(
¬
r
→ ¬
q
)
∧
(
¬
p
∨
q
)
∧
(
¬
r
∨
p
)
Give a succinct description of which combinations of input values work, rather
than the whole truth table.
2.
[6 points] Translating notation into English
Suppose we define:
•
C
(
x
)
is “x takes a potion class.”
•
Q
(
x
)
is “x plays Quidditch .”
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 Fall '07
 fleck
 Siebel

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