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

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

Conjunction Truth Table Click on speaker for audio 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

Disjunction Click on speaker for audio 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

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

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

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

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)

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

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

Conditional Click on speaker for audio 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

Biconditional 5 6 4 7 2 3 1 F T case 4 case 3 case 2 case 1 p) (q q) Click on speaker for audio 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

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