Unit 3 Answers
1.
- Yes, True
- Yes, False
- No
- Yes, False
- Yes, True
- No
- Yes, False
2.
- Norfolk is not the capital of Virginia.
- Food is expensive in th United States.
- 3 + 5
7.
- The summer in Illinois is not hot or (the summer in Illinois is) not sunny.
3. a) p
b) p q
c) q
p
d) q p
4. a) True (because the condition is false)
b) True (because the condition is false)
c) False
d) True
5.
- Converse: "If I stay home, then it snows today.
"
Contrapositive:
"If I do not stay home, then it does not snow today. quot;
- Converse: "If we play the game, then it is sunny."
Contrapositive: "If we don't play the game, then it is not sunny."
- Converse: "If a positive integer has no divisors other than 1 and
itself then it is a prime."
Contrapositive: "If a positive integer has a divisors other than 1 and
itself then it is not a prime.
6.
a)
b)
p q |
q |
p q |
(p q) q |
T T |
F |
T |
T |
T F |
T |
T |
F |
F T |
F |
F |
T |
F F |
T |
T |
F |
c)
p q |
p q |
q |
p |
q
p |
(p q) ( q p) |
T T |
T |
F |
F |
T |
T |
T F |
F |
T |
F |
F |
T |
F T |
T |
F |
T |
T |
T |
F F |
T |
T |
T |
T |
T |