1. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 1 3 3 Logic The Study of What’s True or False or Somewhere in Between

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 2 The Conditional and Biconditional 3.3 Construct truth tables for conditional statements Identify logically equivalent forms of a conditional (continued on next slide)

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 3 Use alternative wording to write conditionals Construct truth tables for biconditional statements The Conditional and Biconditional 3.3

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 4 The Conditional There is only one way a conditional (“if...then”) can be false. wbwb (continued on next slide)

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 5 The Conditional There is only one way a conditional (“if...then”) can be false. wbwb (continued on next slide)

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 6 The Conditional There is only one way a conditional (“if...then”) can be false. wbwb (continued on next slide)

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 7 The Conditional There is only one way a conditional (“if...then”) can be false. wbwb

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 8 The Conditional Summary – Conditional Truth Table

9. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 9 The Conditional

10. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 10 The Conditional We can build truth tables for statements that combine conditionals with the previously-discussed connectives. (example on next slide)

11. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 11 The Conditional Example: Solution:

12. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 12 Derived Forms of a Conditional The converse, inverse, and contrapositive are three derived forms of a conditional.

13. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 13 Derived Forms of a Conditional

14. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 14 Derived Forms of a Conditional Example: Converse: Inverse: (continued on next slide)

15. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 15 Derived Forms of a Conditional Example: Converse:

16. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 16 Derived Forms of a Conditional Example: Solution:

17. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 17 Alternative Wording of Conditionals (example on next slide)

18. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 18 Derived Forms of a Conditional Example: (solution on next 2 slides)

19. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 19 Derived Forms of a Conditional Solution: (continued on next slide)

20. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 20 Derived Forms of a Conditional Solution:

21. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 21 The Biconditional The biconditional means that two statements say the same thing. We symbolize the biconditional as (example on next slide)

22. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.3, Slide 22 The Biconditional Example: Solution: