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Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 1
33 Logic
The Study of What’s True or False or Somewhere in Between
Copyright © 2014, 2010, 2007 Pearson Education, Inc.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)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.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
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.
w b
(continued on next slide)
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.
w b
(continued on next slide)
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.
w b
(continued on next slide)
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.
w b
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 8
The Conditional
• Summary – Conditional Truth Table
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 9
The Conditional
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)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 11
The Conditional
• Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 12
The Conditional
• Example:
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 13
Derived Forms of a Conditional
• The converse, inverse, and contrapositive are three derived forms of a conditional.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 14
Derived Forms of a Conditional
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 15
Derived Forms of a Conditional
• Example:
Converse:
Inverse:
m d
m dd m
m d
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 16
Derived Forms of a Conditional
• Example:
Converse:
m d
m dd m
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 17
Derived Forms of a Conditional
• Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 18
Derived Forms of a Conditional
• Example:
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 19
Alternative Wording of Conditionals
(example on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 20
Derived Forms of a Conditional
• Example:
(solution on next 2 slides)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 21
Derived Forms of a Conditional
• Solution:
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 22
Derived Forms of a Conditional
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 23
The Biconditional
• The biconditional means that two statements say the same thing.
• We symbolize the biconditional as .p q
(example on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 24
The Biconditional
• Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.3, Slide 25
The Biconditional
• Example:
• Solution:
