1. Introduction to Symbolic Logic
2-Ext
Introduction to Symbolic Logic
Lesson Presentation
Holt Geometry

2. Objectives Analyze the truth value of conjunctions and disjunctions.
Construct truth tables to determine the truth value of logical statements.

3. Vocabulary
compound statement
conjunction
disjunction
truth table

4. Symbolic logic is used by computer programmers, mathematicians, and philosophers to analyze the truth value of statements, independent of their actual meaning.
A compound statement is created by combining two or more statements. Suppose p and q each represent a statement. Two compound statements can be formed by combining p and q: a conjunction and a disjunction.

5. A conjunction is true only when all of its parts are true
A conjunction is true only when all of its parts are true. A disjunction is true if any one of its parts is true.

6. Example 1: Analyzing Truth Values of Conjunctions and Disjunctions
Use p, q, and r to find the truth value of each compound statement.
p: The month after April is May.
q: The next prime number after 13 is 17.
r: Half of 19 is 9.
A. p  q
Both p and q are true, therefore the disjunction is true.
B. q  r
Since r is false the conjunction is false.

7. Check It Out! Example 1
Use p, q, and r to find the truth value of each compound statement.
p: Washington, D.C., is the capital of the United States.
q: The day after Monday is Tuesday.
r: California is the largest state in the United States.
A. r  p
Since p is true the disjunction is true.
B. p  q
Since both p and q are true the conjunction is true.

8. A table that lists all possible combinations of truth values for a statement is called a truth table. A truth table shows you the truth value of a compound statement, based on the possible truth values of its parts. p q
p  q
p  q
p  q T F

9. Make sure you include all possible combinations of truth values for each piece of the compound statement.
Caution
The negation (~) of a statement has the opposite truth value.
Remember!

10. Example 2: Constructing Truth Tables for Compound Statements
Construct a truth table for the compound statement ~p  ~q. p q ~p ~q
~p  ~q
T T F F F
T F F T T
F T T F T
F F T T T

11. u v ~u ~v ~u  ~v T T F F F T F F T F F T T F F F F T T T
Check It Out! Example 2
Construct a truth table for the compound statement ~u  ~v. u v ~u ~v
~u  ~v
T T F F F
T F F T F
F T T F F
F F T T T