Unit 3 Answers

1.

1. Yes, True
2. Yes, False
3. No
4. Yes, False
5. Yes, True
6. No
7. Yes, False

2.

1. Norfolk is not the capital of Virginia.
2. Food is expensive in th United States.
3. 3 + 5 7.
4. 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.

1. Converse: "If I stay home, then it snows today. " 
   Contrapositive: "If I do not stay home, then it does not snow today. quot;
2. Converse: "If we play the game, then it is sunny."  
   Contrapositive: "If we don't play the game, then it is not sunny."
3. 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)

p	p	p p
T	F	F
F	T	F

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