Worksheet 5. (Sec 3.4-3.7) Please indicate the most suitable answer on blank near the right margin.
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct a truth table for the statement.
1) ~(q
A)
C)
2) ~(p
~ p)
1)
p
T
T
F
F
q ~ p q ~ p ~(q ~ p)
T F
F
T
F F
F
T
T T
T
F
F T
T
F
p
T
T
F
F
q ~ p q ~ p ~(q ~ p)
T F
T
F
F F
F
T
T T
F
T
F T
F
T
q)
(p
A) p
q
T
T
F
F
T
F
T
F
C) p
q
T
T
F
F
T
F
T
F
B)
D)
p
T
T
F
F
q ~ p q ~ p ~(q ~ p)
T F
F
T
F F
T
F
T T
T
T
F T
T
F
p
T
T
F
F
q ~ p q ~ p ~(q ~ p)
T F
F
T
F F
T
F
T T
T
F
F T
T
F
2)
~q)
~(p
q)
(p
~q)
T
F
F
F
~(p
q)
(p
~q)
T
T
T
T
1
B) p
q
T
T
F
F
T
F
T
F
D) p
q
T
T
F
F
T
F
T
F
~(p
q)
(p
~q)
T
F
T
T
~(p
q)
(p
T
F
F
T
~q)
Construct a truth table for the given statement and then determine if the statement is a tautology.
3) [ (p
A)
B)
C)
D)
~ q)
q]
~p
3)
p
T
T
F
F
q
T
F
T
F
~ q p ~ q (p
F
T
T
F
F
F
T
F
~ q)
T
F
F
F
q ~ p [ (p
F
F
T
T
~ q)
T
T
T
T
q]
p
T
T
F
F
q
T
F
T
F
~ q p ~ q (p
F
F
T
T
F
T
T
T
~ q)
F
F
T
F
q ~ p [ (p
F
F
T
T
~ q)
F
F
T
T
q]
p
T
T
F
F
q
T
F
T
F
~ q p ~ q (p
F
F
T
T
F
T
T
T
~ q)
F
F
T
F
q ~ p [ (p
F
F
T
T
~ q)
T
T
T
T
q]
p
T
T
F
F
q
T
F
T
F
~ q p ~ q (p
F
F
T
T
F
T
T
T
~ q)
F
T
F
F
q ~ p [ (p
F
F
T
T
~ q)
T
T
T
T
q]
2
~p
Is a tautology.
~p
Is not a tautology.
~p
Is a tautology.
~p
Is a tautology.
4) ( ~ p
A)
B)
C)
D)
q)
(~ p
q)
4)
p
T
T
F
F
q ~ p ~p
T F
F
F F
F
T T
T
F T
F
q ~p
T
F
T
T
q (~p
p
T
T
F
F
q ~ p ~p
T F
F
F F
F
T T
T
F T
F
q ~p
T
F
T
T
q (~p
p
T
T
F
F
q ~ p ~p
T F
F
F F
F
T T
T
F T
F
q ~p
T
F
T
T
q (~p
p
T
T
F
F
q ~ p ~p
T F
F
F F
F
T T
T
F T
F
q ~p
F
F
T
F
q (~p
q)
F
F
T
F
(~ p
q)
T
F
T
T
(~ p
q)
T
T
T
T
(~ p
q)
F
F
T
F
(~ p
q)
Is not a tautology.
q)
Is not a tautology.
q)
Is a tautology.
q)
Is not a tautology.
3
Construct a truth table for the given statement.
5) (p
~ q)
A)
B)
C)
D)
( ~q
~ p)
5)
p
T
T
F
F
q ~q p
~ q ~ p ~q ~ p (p
T F
F
F
T
F T
T
F
F
T F
T
T
T
F T
F
T
T
~ q)
p
T
T
F
F
q ~q p
~ q ~ p ~q ~ p (p
T F
F
F
T
F T
T
F
F
T F
T
T
T
F T
F
T
T
~ q)
p
T
T
F
F
q ~q p
~ q ~ p ~q ~ p (p
T F
F
F
T
F T
T
F
F
T F
T
T
T
F T
F
T
T
~ q)
p
T
T
F
F
q ~q p
~ q ~ p ~q ~ p (p
T F
F
F
T
F T
T
F
F
T F
T
T
F
F T
F
T
T
~ q)
4
T
T
T
T
T
F
T
T
F
F
T
F
T
F
F
T
( ~q
~ p)
( ~q
~ p)
( ~q
~ p)
( ~q
~ p)
Construct a truth table for the statement. Then determine if the statement is a tautology.
6) (q
p)
A)
B)
C)
D)
(~ p
q)
6)
p
T
T
F
F
q q p ~p ~p
T
T
F
T
F
T
F
F
T
F
T
T
F
T
T
T
q (q
p
T
T
F
F
q q p ~p ~p
T
T
F
T
F
T
F
F
T
F
T
T
F
T
T
T
q (q
p
T
T
F
F
q q p ~p ~p
T
T
T
T
F
T
F
F
T
F
T
T
F
F
T
T
q (q
p
T
T
F
F
q q p ~p ~p
T
T
F
T
F
F
F
F
T
T
T
T
F
T
T
T
q (q
p)
p)
p)
p)
T
F
T
T
T
F
F
T
F
F
F
T
T
T
T
T
(~ p
q)
Is not a tautology.
(~ p
q)
Is not a tautology.
(~ p
q)
Is not a tautology.
(~ p
q)
Is a tautology.
5
The table shows ice cream cone sales at an ice cream shop. Let p and q represent the following statements:
p: Vanilla is the best-selling flavor.
q: Chocolate chip outsold strawberry by 13,000 cones.
Ice Cream Sold One Year
Sales in Thousands
Flavor
of Cones
chocolate
33
vanilla
31
chocolate chip
27
strawberry
14
coffee
8
butterscotch
5
7) Write the symbolic statement below in words. Then use the table to determine the truth value of
the statement.
~q ~p
7)
A) If chocolate chip did not out sell strawberry by 13,000 cones, then vanilla was not the
best-selling flavor.
Truth value: False
B) If chocolate chip out sold strawberry by 13,000 cones, then vanilla was not the best-selling
flavor.
Truth value: True
C) If chocolate chip did not out sell strawberry by 13,000 cones, then vanilla was the best-selling
flavor.
Truth value: True
D) If chocolate chip did not out sell strawberry by 13,000 cones, then vanilla was not the
best-selling flavor.
Truth value: True
Use a truth table to determine whether the two statements are equivalent.
8) ~(q
p) and q
8)
~p
A) Yes
B) No
Select the statement that is equivalent to the given statement.
9) I ate a pickle or a hot dog.
9)
A) If I did not eat a pickle, then I ate a hot dog.
B) If I ate a pickle, then I ate a hot dog.
C) If I did not a pickle, then I did not eat a hot dog.
D) If I ate a pickle, then I did not eat a hot dog.
6
Write the equivalent contrapositive of the statement.
10) If he is not working in China, then he is vacationing in England.
10)
A) If he is vacationing in China, then he is not working in England.
B) If he is not vacationing in China, then he is working in England.
C) If he is not vacationing in England, then he is working in China.
D) If he is working in China, then he is not vacationing in England.
Write the nonequivalent converse and inverse of the statement.
11) If you are getting a haircut, then you are not studying.
11)
A) converse: If you are not studying, then you are getting a haircut.
inverse: If you are not getting a haircut, then you are studying
B) converse: If you are not getting a haircut, then you are studying
inverse: If you are not studying, then you are getting a haircut.
C) converse: If you are not studying, then you are getting a haircut.
inverse: If you are getting a haircut, then you are not studying
D) converse: If you are studying, then you are not getting a haircut.
inverse: If you are not getting a haircut, then you are studying
12) If Nathan performs in New York, then he performs in the United States.
A) converse: If Nathan performs in the United States, then he performs in New York.
inverse: If Nathan does not perform in New York, then he does not perform in the United
States.
B) converse: If Nathan does not perform in the United States, then he does not perform in New
York.
inverse: If Nathan does not perform in New York, then he does not perform in the United
States.
C) converse: If Nathan does not perform in the United States, then he does not perform in New
York.
inverse: If Nathan does not perform in New York, then he performs in the United States.
D) converse: If Nathan performs in the United States, then he performs in New York.
inverse: If Nathan does not perform in New York, then he performs in the United States
7
12)