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Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.2, Slide 1 3 Logic The Study of Whats True or False or Somewhere in Between 3.

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Presentation on theme: "Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.2, Slide 1 3 Logic The Study of Whats True or False or Somewhere in Between 3."— Presentation transcript:

1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.2, Slide 1 3 Logic The Study of Whats True or False or Somewhere in Between 3

2 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.2, Slide 2 Truth Tables3.2 Learn the truth tables for the five fundamental connectives Compute truth tables for compound statements (continued on next slide)

3 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.2, Slide 3 Truth Tables3.2 Determine when statements are logically equivalent State and apply DeMorgans laws.

4 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 4 Truth Tables We want to know if a pair of similar statements such as and mean the same thing. We use truth tables to determine when compound statements are true and when they are false, and whether a pair of statements have the same meaning.

5 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 5 Truth Tables

6 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 6 Truth Tables If p is true, then ~p is false. If p is false, then ~p is true. (example on next slide)

7 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 7 Truth Tables Example:

8 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 8 Truth Tables A conjunction is true only when both of its components are true. (example on next slide)

9 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 9 Truth Tables Example: (solution on next slide)

10 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 10 Truth Tables Example: (solution on next slide)

11 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 11 Truth Tables Solution:

12 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 12 Truth Tables A disjunction is false only when both p and q are false. (example on next slide)

13 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 13 Truth Tables Example: (solution on next slide)

14 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 14 Truth Tables Solution:

15 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 15 Truth Tables Because of their similar structures, there are parallels that occur in logic and set theory. Often if a result is true for set theory, then a similar result also holds for logic (and vice versa).

16 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 16 Compound Statements We use truth tables to find the logical values of complex statements. Example: Compute a truth table for (solution on next 3 slides)

17 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 17 Compound Statements (solution continued on next slide)

18 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 18 Compound Statements (solution continued on next slide)

19 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 19 Compound Statements If p is false and q is true, line 3 tells us that is false.

20 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 20 Compound Statements Definition: If the final column of a truth table contains all Ts, then the statement is always true. Such a statement is called a tautology. Example: This contestant will win or will not win.

21 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 21 Compound Statements How many lines should your truth table have?

22 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 22 Logically Equivalent Statements Logically equivalent statements express the same meaning. (example on next slide)

23 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 23 Logically Equivalent Statements Example: (solution on next slide)

24 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 24 Logically Equivalent Statements Solution: The two statements are logically equivalent.

25 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 25 DeMorgans Laws (example on next slide)

26 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 26 DeMorgans Laws Example:

27 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 27 DeMorgans Laws

28 Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.2, Slide 28 Truth Tables: Alternative Method


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