Thinking
Mathematically
Logic
3.3 Truth Tables for Negation, Conjunction, and Disjunction
Definitions of Negation,
Conjunction, and Disjunction
1. Negation ~: not
The negation of a statement has the opposite
truth value from the statement.
2. Conjunction ^ : and
The only case in which a conjunction is true is
when both component statements are true.
3. Disjunction: V : or
The only case in which a disjunction is false is
when both component statements are false.
Examples: Negation, Conjunction,
Disjunction
Exercise Set 3.3 #3, 7, 11
• p: 4 + 6 = 10
• q: 5 x 8 = 80
What is the truth value of the following statements?
o
o
o
p^q
~p ^ ~q
p V ~q
What if you didn’t know the truth values of the
component statements p and q. How could you
view the truth value of the compound statement.
Truth Tables
• A truth table list all possible truth values for a
compound statement based on the truth values of
its component (simple) statements
• A complete truth table must have one row for each
possible combination of truth values of its
component statements.
• If a compound statement has n component
statements, then the complete truth table has 2n
rows.
“Truth Tables” - Negation
If a statement is true then its negation is false
and if the statement is false then its negation
is true. This can be represented in the form
of a table called a “truth table.”
p
T
F
~p
F
T
Truth Tables -- Conjunction
A conjunction is true only when both
simple statements are true.
p
T
T
F
F
q
T
F
T
F
pq
T
F
F
F
Truth Tables -- Disjunction
A disjunction is false only when both
component statements are false.
p
T
T
F
F
q
T
F
T
F
pq
T
T
T
F
Examples
Exercise Set 3.3 #21, #27, #31
Construct a truth table for
~(p V q)
~(~ p V q)
~ p V (p ^ ~q)
Thinking
Mathematically
Logic
3.3 Truth Tables for Negation, Conjunction, and Disjunction