3
Logic
The Study of What’s True
or False or Somewhere in
Between
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 1
3.3 The Conditional and
Biconditional
• Construct truth tables for
conditional statements
• Identify logically equivalent forms
of a conditional
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 2
3.3 The Conditional and
Biconditional
• Use alternative wording to write
conditionals
• Construct truth tables for
biconditional statements
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 3
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 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
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 7
The Conditional
• Summary – Conditional Truth Table
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 8
The Conditional
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 9
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 10
The Conditional
• Example:
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Section 3.3, Slide 11
The Conditional
• Example:
• Solution:
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.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 13
Derived Forms of a Conditional
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 14
Derived Forms of a Conditional
• Example:
m
d
m® d
Converse: d  m
Inverse: ∼ m ®∼ d
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 15
Derived Forms of a Conditional
• Example:
m
d
md
Contrapositive: ∼ d ®∼ m
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 16
Derived Forms of a Conditional
• Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 17
Derived Forms of a Conditional
• Example:
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 18
Alternative Wording of Conditionals
(example on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 19
Derived Forms of a Conditional
• Example:
(solution on next 2 slides)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 20
Derived Forms of a Conditional
• Solution:
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 21
Derived Forms of a Conditional
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 22
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 23
The Biconditional
• Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 24
The Biconditional
• Example:
• Solution:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 3.3, Slide 25