3 2 Truth Tables for Negation Conjunction and

3. 2 Truth Tables for Negation, Conjunction, and Disjunction Copyright © 2005 Pearson Education, Inc.

Truth Table n 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 Click on speaker for audio The symbol ^ is read as “and” 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 Click on speaker for audio The symbol V is read as “or” 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) Click on speaker for audio 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 Copyright © 2005 Pearson Education, Inc. 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 F F F T T Copyright © 2005 Pearson Education, Inc. Slide 3 -7

Check it out n n 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 n n n 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 Click on speaker for audio p -> q is read as “if p then 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 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 Click on speaker for audio n The biconditional statement, or, symbolically means that and Take these 2 columns to get column 7 p q (p case 1 T T T T T case 2 T F F F F T T case 3 F T T F F case 4 F F F T F T F 1 3 2 7 4 6 5 order of steps Copyright © 2005 Pearson Education, Inc. q) (q p) Slide 3 -12

Next steps n n 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