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Assign Yourself and Do Now

This resource provides a comprehensive explanation of truth tables, focusing on tautologies, logical contradictions, and their applications. You will learn how to construct truth tables for compound propositions, identify their logical classifications, and understand the implications of conjunctions and disjunctions. Examples, including scenarios with Sponge Bob and Brittany, illustrate key concepts. By the end, you will be able to analyze propositions, negate them, and determine logical equivalence while preparing for upcoming quizzes and assignments.

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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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