1. Truth Tables for Negation, Conjunction, and Disjunction
3.2
Truth Tables for Negation, Conjunction, and Disjunction

2. Truth Table
A truth table is used to determine when a compound statement is true or false.

3. Conjunction Truth Table
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The symbol ^ is read as “and”
The conjunction is true only when both p and q are true. F
Case 4 T
Case 3
Case 2
Case 1 q p

4. Disjunction
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The symbol V is read as “or”
The disjunction is true when either p is true, q is true, or both p and q are true. F
Case 4 T
Case 3
Case 2
Case 1 q p

5. 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. F
Case 4 T
Case 3
Case 2
Case 1 q p

6. 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 T F
Case 4
Case 3
Case 2
Case 1 ~q q p

7. 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 F

8. 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)

9. 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

10. Truth Tables for the Conditional and Biconditional
3.3
Truth Tables for the Conditional and Biconditional

11. Conditional
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p -> q is read as “if p then q”
The conditional statement is true in every case except when p is a true statement and q is a false statement. T F
Case 4
Case 3
Case 2
Case 1 q p

12. Biconditional 5 6 4 7 2 3 1 F T case 4 case 3 case 2 case 1 p) (q q)
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The biconditional statement, means that and or, symbolically
Take these 2 columns to get column 7 5 6 4 7 2 3 1
order of steps F T
case 4
case 3
case 2
case 1 p) (q q) (p q p

13. 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