Sec' 3'2 Truth Tables, Conjunction

1
Sec. 3.2 Truth Tables, Conjunction Disjunction
Introduction to Alice in Wonderland by Walt
Disney with mention of Charles Dodgson (Lewis
Carroll)
www.youtube.com/watch?vGpeNMNX-_oo
2nd Intro by Alice
http//www.youtube.com/watch?vQtP60NmDKqcfeature
related
Mad Tea Party (4min)
www.youtube.com/watch?vz0q-9aFzIbUfeaturerelate
d
2
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p

3
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p

4
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 2

5
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T 2

6
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T 2 F

7
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F

8
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

9
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q



10
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 2
3 4

11
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T 2
3 4

12
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2
3 4

13
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2 T
3 4

14
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2 T F
3 4

15
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2 T F
3 F 4

16
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2 T F
3 F T 4

17
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2 T F
3 F T 4 F

18
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2 T F
3 F T 4 F F

19
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T 2 T F
3 F T 4 F F

ANSWER
20
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T T 2
T F T 3 F T
F 4 F F F

ANSWER
21
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T T T 2
T F T F 3 F T
F T 4 F F F
F
1 T
2 T 3
F 4
F
ANSWER
22
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T T T 2
T F T F 3 F T
F T 4 F F F
F
ANSWER
23
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T T T T 2
T F T F F 3 F T
F F T 4 F F F F
F
ANSWER
24
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T T T T 2
T F T F F 3 F T
F F T 4 F F F F
F
ANSWER
25
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T T T T 2
T F T F F 3 F T
F F T 4 F F F F
F
ANSWER
26
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction
p q p q
1 T T T T T 2
T F T F F 3 F T
F F T 4 F F F F
F
ANSWER
27
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction Disjunction
p q p q p
q p q
1 T T T T T 1 T T
2 T F T F F 2 T F 3
F T F F T 3 F T 4 F F
F F F 4 F F
ANSWER
ANSWER
28
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction Disjunction
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F 2
T F T T F 3 F T F F
T 3 F T F T T 4 F F F F
F 4 F F F F F
ANSWER
ANSWER
29
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction Disjunction
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F 2
T F T T F 3 F T F F
T 3 F T F T T 4 F F F F
F 4 F F F F F
ANSWER
ANSWER
30
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction Disjunction
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F 2
T F T T F 3 F T F F
T 3 F T F T T 4 F F F F
F 4 F F F F F
ANSWER
ANSWER
31
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction Disjunction
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F 2
T F T T F 3 F T F F
T 3 F T F T T 4 F F F F
F 4 F F F F F
ANSWER
ANSWER
32
Sec. 3.2 Truth Tables, Conjunction Disjunction
Negation
p p
1 T F 2 F T

Conjunction Disjunction
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F 2
T F T T F 3 F T F F
T 3 F T F T T 4 F F F F
F 4 F F F F F
ANSWER
ANSWER
33
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F T T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T F T 3 F
T T F 4 F F T F F 4
F F F F
T T F T

ANSWER
ANSWER
34
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F T 1 T T
F T 2 T F F F 2 T
F F T 3 F T T F 3 F
T T F 4 F F T F 4
F F F F
T T F T

ANSWER
ANSWER
35
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F T T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T F T 3 F
T T F 4 F F T F F 4
F F F F
T T F T

ANSWER
ANSWER
36
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T F T 3 F
T T F 4 F F T F F 4
F F F F
T T F T

ANSWER
ANSWER
37
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T F T 3 F
T T F 4 F F T F F 4
F F F F
T T F T

ANSWER
ANSWER
38
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
T T F T

ANSWER
ANSWER
39
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
T T F T

ANSWER
ANSWER
40
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
T T F T

ANSWER
ANSWER
41
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
42
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
43
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
44
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
45
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
46
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
47
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
48
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
49
Sec. 3.2 Truth Tables, Conjunction Disjunction
ex. Construct a truth table for the following
p q p q p
q ( p q)
1 T T F F T 1 T T
F T 2 T F F F F 2 T
F F T 3 F T T T T 3 F
T T F 4 F F T F F 4
F F F F
F T F T
T T F T

ANSWER
ANSWER
50
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T 2 T F 3 F T 4
F F

ANSWER
51
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T 2 T F 3 F T 4
F F

ANSWER
p You get an A in math class
52
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T 2 T F 3 F T 4
F F

ANSWER
p You get an A in math class q I will
buy you a car
53
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T 2 T F 3 F T 4
F F

ANSWER
p You get an A in math class q I will
buy you a car
hence the conditional statement
54
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T 2 T F 3 F T 4
F F

ANSWER
p You get an A in math class q I will
buy you a car
hence the conditional statement
If you get an A in math class, then I will buy
you a car.
55
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T T T T 2 T F T F
F 3 F T F T T 4 F F F T
F

ANSWER
p You get an A in math class q I will
buy you a car
hence the conditional statement
If you get an A in math class, then I will buy
you a car.
56
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T T T T 2 T F T F
F 3 F T F T T 4 F F F T
F

ANSWER
p You get an A in math class q I will
buy you a car
hence the conditional statement
If you get an A in math class, then I will buy
you a car.
57
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T T T T 2 T F T F
F 3 F T F T T 4 F F F T
F

ANSWER
p You get an A in math class q I will
buy you a car
hence the conditional statement
If you get an A in math class, then I will buy
you a car.
58
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T T T T 2 T F T F
F 3 F T F T T 4 F F F T
F

ANSWER
p You get an A in math class q I will
buy you a car
hence the conditional statement
If you get an A in math class, then I will buy
you a car.
59
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional
p q p q
1 T T T T T 2 T F T F
F 3 F T F T T 4 F F F T
F

ANSWER
p You get an A in math class q I will
buy you a car
hence the conditional statement
If you get an A in math class, then I will buy
you a car.
60
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional Biconditional
p q p q p
q p q
1 T T T T T 1 T T
2 T F T F F 2 T
F 3 F T F T T 3 F T
4 F F F T F 4 F F


ANSWER
ANSWER
61
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional Biconditional
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F
2 T F T T F 3 F T F T
T 3 F T F T T 4 F F F
T F 4 F F F F F

ANSWER
ANSWER
62
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional Biconditional
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F
2 T F T T F 3 F T F T
T 3 F T F T T 4 F F F
T F 4 F F F F F

ANSWER
ANSWER
63
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional Biconditional
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F
2 T F T F F 3 F T F T
T 3 F T F T T 4 F F F
T F 4 F F F F F

ANSWER
ANSWER
64
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional Biconditional
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F
2 T F T F F 3 F T F T
T 3 F T F F T 4 F F F
T F 4 F F F F F

ANSWER
ANSWER
65
Sec. 3.3 Truth Tables, Conditional
Biconditional
Conditional Biconditional
p q p q p
q p q
1 T T T T T 1 T T
T T T 2 T F T F F
2 T F T F F 3 F T F T
T 3 F T F F T 4 F F F
T F 4 F F F T F

ANSWER
ANSWER
66
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
67
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
68
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
69
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
70
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
71
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
72
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
73
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
74
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
75
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
76
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q p q p q q p
1 T T F T T 1 T T
F T F 2 T F F F F 2
T F T F F 3 F T T T
T 3 F T F T T 4 F F
T T F 4 F F T T T
We know
ANSWER
Conditional
Disjunction
ANSWER
p q p q
p q p q
1 T T T 2 T F T 3 F T
T 4 F F F
1 T T T 2 T F F 3
F T T 4 F F T
77
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
78
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
79
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
80
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
81
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
82
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
83
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
84
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
85
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
86
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
87
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
88
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
89
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
90
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T 2 T F F T T 2
T F 3 F T F T T
3 F T 4 F F F T
F 4 F F
ANSWER
ANSWER
Tautology
91
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F 2 T F F T T
2 T F T T 3 F T F T
T 3 F T F T 4 F F
F T F 4 F F F F

ANSWER
ANSWER
Tautology
92
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
ANSWER
ANSWER
Tautology
93
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F 2 T F F T
T 2 T F T T T F
3 F T F T T 3 F
T F T F F 4 F F F T
F 4 F F F F T F
ANSWER
ANSWER
Tautology
94
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F 2 T F F T
T 2 T F T T T F
3 F T F T T 3 F
T F T F F 4 F F F T
F 4 F F F F T F
ANSWER
ANSWER
Tautology
95
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F 2 T F F T
T 2 T F T T T F
3 F T F T T 3 F
T F T F F 4 F F F T
F 4 F F F F T F
ANSWER
ANSWER
Tautology
96
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F 2 T F F T
T 2 T F T T T F
3 F T F T T 3 F
T F T F F 4 F F F T
F 4 F F F F T F
ANSWER
ANSWER
Tautology
97
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T F T
F 3 F T F T T 3
F T F T F F F T 4 F F
F T F 4 F F F F T
F F F
ANSWER
ANSWER
Tautology
98
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T F T
F 3 F T F T T 3
F T F T F F F T 4 F F
F T F 4 F F F F T
F F F
ANSWER
ANSWER
Tautology
99
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T F T
F 3 F T F T T 3
F T F T F F F T 4 F F
F T F 4 F F F F T
F F F
ANSWER
ANSWER
Tautology
100
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T F T
F 3 F T F T T 3
F T F T F F F T 4 F F
F T F 4 F F F F T
F F F
ANSWER
ANSWER
Tautology
101
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T F T
F 3 F T F T T 3
F T F T F F F T 4 F F
F T F 4 F F F F T
F F F
ANSWER
ANSWER
Tautology
102
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T F T
F 3 F T F T T 3
F T F T F F F T 4 F F
F T F 4 F F F F T
F F F
ANSWER
ANSWER
Tautology
103
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T T
F 3 F T F T T
3 F T F T F F F T 4 F F
F T F 4 F F F F T
F F F
ANSWER
ANSWER
Tautology
104
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T T
F 3 F T F T T
3 F T F T F F T 4 F F
F T F 4 F F F F
T F F F
ANSWER
ANSWER
Tautology
105
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T T
F 3 F T F T T
3 F T F T F F T 4 F F
F T F 4 F F F F
T F F
ANSWER
ANSWER
Tautology
106
Sec. 3.3 Truth Tables, Conditional
Biconditional
ex. Construct a truth table for the following
p q (p q) (p q) p
q (p ? q) (p ? q)
1 T T T T T 1 T
T T F F F T 2 T F F T
T 2 T F T T T F
F 3 F T F T T 3 F
T F T F F F 4 F F F T
F 4 F F F F T F
T
1 T T T T T 1 T
T T F F F T T 2 T F F
T T 2 T F T T T T
F 3 F T F T T
3 F T F T F F T 4 F F
F T F 4 F F F F
T F F
ANSWER
ANSWER
Tautology
Self-Contradiction
107
Sec. 3.3 Truth Tables, Conditional
Biconditional
Review
Conjunction Disjunction
p q p q p
q p q
1 T T T 1 T T T 2 T
F F 2 T F T 3 F
T F 3 F T T 4 F
F F 4 F F F
Conditional Biconditional
p q p q p
q p q
1 T T T 1 T T T 2 T
F F 2 T F F 3 F
T T 3 F T F 4 F
F T 4 F F T