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3.2

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  1. 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. p q Case 1 T T T Case 2 T F F Case 3 F T F Case 4 F F F Conjunction Truth Table Click on speaker for audio The symbol ^ is read as “and” The conjunction is true only when bothp and q are true.

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

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

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

  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.

  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. 3.3 Truth Tables for theConditional and Biconditional

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

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

  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

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