1. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, 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 3.1, Slide 2 Statements, Connectives, and Quantifiers 3.1 Identify statements in logic Represent statements symbolically using five connectives (continued on next slide)

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide 3 Statements, Connectives, and Quantifiers 3.1 Understand the difference between the universal and existential quantifiers Write the negations of quantified statements

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 4 Statements in Logic In symbolic logic, we only care whether statements are true or false – not their content.

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 5 Statements in Logic Examples of statements:

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 6 Statements in Logic Examples of non-statements:

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 7 Statements in Logic Note that (a)-(d) fall into 2 categories: –Simple statements containing a single idea ((a) and (c)). –Compound statements containing several ideas ((b) and (d)).

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 8 Statements in Logic

9. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 9 Connectives The connectives used in logic generally fall into five categories: –Negation –Conjunction –Disjunction –Conditional –Biconditional

10. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 10 Connectives (example on next slide)

11. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 11 Connectives Negation Example:

12. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 12 Connectives Example:

13. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 13 Connectives

14. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 14 Connectives Example:

15. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 15 Connectives Example:

16. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 16 Connectives Example:

17. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 17 Connectives

18. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 18 Quantifiers A quantifier tells us “how many” and fall into two categories. –Universal quantifiers –Existential quantifiers

19. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 19 Quantifiers

20. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 20 Quantifiers

21. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 21 Negating Quantifiers Suppose we want to negate the statement “All professional athletes are wealthy.” (universal) Correct: “Some athletes are not wealthy” or “Not all athletes are wealthy.” (both existential) Incorrect: “All athletes are not wealthy.” (universal)

22. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 22 Negating Quantifiers Negate the statement “Some students will get a scholarship.” (existential) Correct: “No students will get a scholarship.” (universal) Incorrect: “Some students will not get a scholarship.” (existential)

23. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 23 Negating Quantifiers