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3.2

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. 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.

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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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