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Assign Yourself and Do Now

Assign Yourself and Do Now. Thursday, January 10, 2013. Truth Table. Explanation. It will always be true – since OR means at least one, and they are opposites, one of them will be true always. Do Now Explanation. Truth Tables. In words, p v ¬q:. Truth Table.

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Assign Yourself and Do Now

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

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

  3. Truth Tables

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

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

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

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

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

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

  10. Meaning in Words Truth Table ¬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. ¬p v ¬q

  11. ¬ (p ^ q) Truth Table ¬ p v ¬ q Truth Table If two truth tables have the same end result, then the two statements are logically equivalent. Compare the Two!

  12. Make your columns: p, q, r, ¬ r, p v q, (p v q) ^ ¬ r • The IB will help you by making the table the right size • Because we have three original propositions (p, q, r), we will have 23 = 8 rows below the header. Try the Lizzy Truth Table

  13. Lizzy Truth Table… Finish the Rest!

  14. Lizzy Truth Table Answer

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

  16. 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 HW Check/ Time For HW

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