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Solutions to CS191 Homework One
Winter 2007
Due: Jan. 30, 2007, in class
Section 1.1, p7
Determine whether each sentence in Exercises 18 is a proposition. If the sentence is a
proposition, write its negation. (you are not being asked for the truth values of the
sentences that are propositions.)
Exercise
(3)
For some positive integer
n
, 19340 =
n
⋅
17
Answer:
It is a proposition. Negation: For every positive integer
n
, 19340
≠
n
⋅
17.
Write the truth table of each proposition in Exercises 1926
Exercise
(26)
¬
(
p
∧
q
)
∨
(
¬
q
∨
r
)
Answer
:
p
q
r
(
p
∧
q
)
¬
(
p
∧
q
)
¬
q
(
¬
q
∨
r
)
¬
(
p
∧
q
)
∨
(
¬
q
∨
r
)
T
T
T
T
F
F
T
T
T
T
F
T
F
F
F
F
T
F
T
F
T
T
T
T
T
F
F
F
T
T
T
T
F
T
T
F
T
F
T
T
F
T
F
F
T
F
F
T
F
F
T
F
T
T
T
T
F
F
F
F
T
T
T
T
In exercises 3640, formulate the symbolic expression in words using
p:
Today is Monday.
q:
It is raining.
r:
It is hot.
Exercise
(38)
¬
(
p
∨
q
)
∧
r
Answer
:
1
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View Full Document It is not the case that (today is Monday or it is raining) and it is hot.
(This answer is not clear enough. A better way to say is
It is hot and it is not the case that (today is Monday or it is raining).
In exercises 4752, represent the proposition symbolically by letting
p:
You heard the “Flying Pigs” rock concert.
q:
You heard the “Y2K” rock concert.
r:
You have sore eardrums.
Exercise
(51)
You did not hear the “flying Pigs” rock concert and you did not hear the “Y2K” rock
concert, but you have sore eardrums.
Answer:
¬
p
∧¬
q
∧
r
.
Section 1.2, p16
Assuming that p and r are false and that q and s are true, find the truth value of each proposition
in Exercises 1017.
Exercise
(14)
(
p
→
q
)
→
r
Answer
:
p
→
(
q
→
r
)
= (F
→
T)
→
F
= T
→
F
= F.
In Exercises 3841, write each conditional proposition symbolically. Write the converse and
contrapositive of each proposition symbolically and in words. Also, find the truth value of each
conditional proposition, its converse, and its contrapositive.
Exercise
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This note was uploaded on 04/12/2008 for the course CS 191 taught by Professor Shen during the Winter '06 term at University of MissouriKansas City .
 Winter '06
 Shen

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