1. Assign Yourself and Do Now Thursday, January 10, 2013

2. Do Now Explanation Truth Table p¬p p ∨ ¬p TFT FTT Explanation It will always be true – since OR means at least one, and they are opposites, one of them will be true always.

3. Truth Tables Negation “not” Conjunction “and” Disjunction “or” Exclusive Disjunction “or, not both” pq ¬p¬q ∧∨ TTFFTTF TFFTFTT FTTFFTT FFTTFFF

4. Sponge Bob and Patrick In words, p v ¬q: Sponge Bob lives under the sea or Sponge Bob and Patrick are not friends. Truth Table pq¬qp v ¬q TTFT TFTT FTFF FFTT

5. Under what conditions is p v ¬q true? When Sponge Bob lives under the sea When Spongebob and Patrick are not friends Both

6. New Definitions Tautology A compound proposition is a tautology if all the values in its truth table column are true. Logical Contradiction A compound proposition is a logical contradiction if all the values in its truth table column are false.

7. Determine if p v ¬p is a tautology, a logical contradiction or neither p v ¬p – truth table p¬pp v ¬p TFT FTT Conclusion? It is a tautology because all the values in the p v ¬p column are TRUE.

8. Tautology, Logical Contradiction or Neither? pqp ^ qp v q¬ (p v q)(p ^ q) ^ ¬ (p v q) TTTTFF TFFTFF FTFTFF FFFFTF (p ^ q) ^ ¬ (p v q) is a logical contradiction because all of the values in its column are false.

9. ¬(p^q) Meaning in Words ¬(p^q) = ¬(Brittany likes volleyball and math) = Brittany does not like both volleyball and math (she dislikes at least one). Truth Table pqp ^ q¬(p^q) TTTF TFFT FTFT FFFT

10. ¬p v ¬q Meaning in Words ¬p v ¬q = Brittany does not like volleyball or Brittany does not like math (or both). This is neither a tautology nor a logical contradiction because the last column is not purely T or F. Truth Table pq¬p¬q¬p v ¬q TTFFF TFFTT FTTFT FFTTT

11. Compare the Two! ¬ p v ¬ q Truth Table pq¬p¬q¬p v ¬q TTFFF TFFTT FTTFT FFTTT ¬ (p ^ q) Truth Table pqp ^ q¬(p^q) TTTF TFFT FTFT FFFT If two truth tables have the same end result, then the two statements are logically equivalent.

12. Try the Lizzy Truth Table 1.Make your columns: p, q, r, ¬ r, p v q, (p v q) ^ ¬ r 2.The IB will help you by making the table the right size 3.Because we have three original propositions (p, q, r), we will have 2 3 = 8 rows below the header.

13. Lizzy Truth Table… Finish the Rest! pqr¬ rp v q(p v q) ^ ¬ r TTT TTF TFT TFF FTT FTF FFT FFF

14. Lizzy Truth Table Answer pqr¬ rp v q(p v q) ^ ¬ r TTTFTF TTFTTT TFTFTF TFFTTT FTTFTF FTFTTT FFTFFF FFFTFF

15. For Tomorrow’s Quiz You should be able to: 1.Say if something is/isn’t a proposition. (Tues.) 2.Negate propositions. (Tues.) 3.Use conjunctions (and, ^), disjunctions (at least one, v), exclusive disjunctions (either/or, v). (Wed.) 4.Say if a statement is a tautology, logical contradiction, or neither. (Thurs.) 5.Say if two statements are logically equivalent. (Thurs.)

16. HW Check/ Time For HW P. 540, #1, 2, 3, 4, 6, 8 P. 542 # 1, 2, 3, 4, 5, 6 do a and b. If there is more than one sub question, do i & ii