3.2
Truth Tables for Negation,
Conjunction, and Disjunction
Copyright © 2005 Pearson Education, Inc.
Truth Table
„
A truth table is used to determine when a
compound statement is true or false.
Copyright © 2005 Pearson Education, Inc.
Slide 3-2
Conjunction Truth Table
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The symbol ^ is read as “and”
p
q
p∧ q
Case 1
T
T
T
Case 2
T
F
F
Case 3
F
T
F
Case 4
F
F
F
The conjunction is true only when both p and q are true.
Copyright © 2005 Pearson Education, Inc.
Slide 3-3
Disjunction
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The symbol V is read as “or”
p
q
p∨ q
Case 1
T
T
T
Case 2
T
F
T
Case 3
F
T
T
Case 4
F
F
F
The disjunction is true when either p is true, q is true, or
both p and q are true.
Copyright © 2005 Pearson Education, Inc.
Slide 3-4
Making a truth table
Let’s construct a truth table for p v ~q. This is
read as “p or not q”.
Step 1: Make a table with different possibilities for
p and q .There are 4 different possibilities.
p
q
Case 1
T
T
Case 2
T
F
Case 3
F
T
Case 4
F
F
Copyright © 2005 Pearson Education, Inc.
Slide 3-5
Making a truth table (cont’d)
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Step 2: Now, make a column for ~q (“not” q) since
we want to ultimately find p v ~q
p
q
~q
Case 1
T
T
F
Case 2
T
F
T
Case 3
F
T
F
Case 4
F
F
T
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Slide 3-6
Making a truth table (cont’d)
Step 3: Next, make a column for p v ~q. Use the first and
third columns to decide the truth values for p v ~q
The truth table is now finished.
p
q
~q
p v~q
T
T
F
T
T
F
T
T
F
T
F
F
F
F
T
T
Copyright © 2005 Pearson Education, Inc.
Slide 3-7
Check it out
„
„
Use the truth table above to decide the truth
value of p V ~q if p is false and q is true.
(Answer: p V ~q is false)
Copyright © 2005 Pearson Education, Inc.
Slide 3-8
Next steps
„
„
„
Read Examples 1-6
Work problems 5-13,odds; 43-50,all; 51-54,all
from p. 115 in text
Do online homework for Sec . 3.2
Copyright © 2005 Pearson Education, Inc.
Slide 3-9
3.3
Truth Tables for the
Conditional and Biconditional
Copyright © 2005 Pearson Education, Inc.
Conditional
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p -> q is read as “if p then q”
p
q
p→q
Case 1
T
T
T
Case 2
T
F
F
Case 3
F
T
T
Case 4
F
F
T
The conditional statement p → q is true in every case
except when p is a true statement and q is a false
statement.
Copyright © 2005 Pearson Education, Inc.
Slide 3-11
Biconditional
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„
The biconditional statement, p ↔ q means that
or, symbolically p → q ∧ q → p .
(
) (
)
p → q and q → p,
Take these 2 columns to get column 7
→ q) ∧
q
(p
case 1
T
T
T
T
T
T
T
T
T
case 2
T
F
T
F
F
F
F
T
T
case 3
F
T
F
T
T
F
T
F
F
case 4
F
F
F
T
F
T
F
T
F
1
3
2
7
4
6
5
order of steps
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(q
→ p)
p
Slide 3-12
Next steps
„
„
„
„
Read Examples 1 and 5 only
Work problems 7-13, odds; 71-76, all from p.
125 in text
Do online homework for Sec . 3.3
Do online quiz for 3.2 and 3.3
Copyright © 2005 Pearson Education, Inc.
Slide 3-13