Section 3.3 Truth Tables for Negation, Conjunction and Disjunction

1
Section 3.3 Truth Tables for Negation,
Conjunction and Disjunction

• Thinking Mathematically
• Math 1001

2
Objectives

• Use the definitions of negation, conjunction, and
  disjunction.
• Construct truth tables.
• Use a De Morgan law.

3
Negation

• The negation of a true statement is a false
  statement.
• The negation of a false statement is a true
  statement.
• The next slide will combine the two tables.

p
p
T
F
p
p
F
T
4
Truth Table for Negation

• This truth table presents two cases.
• Since there is only one fact to consider there
  are only two cases.
• The next table looks at the four cases of
  conjunction.

p
p
T
F
F
T
5
Truth Table for Conjunction, , AND
T
Both simple statements are true.
F
The second simple statement is false.
F
The first simple statement is false.
F
Both simple statements are false.
6
Truth Table for Disjunction, V, OR
T
Both simple statements are true.
At least one simple statement is true.
T
At least one simple statement is true.
T
Both simple statements are false.
F
7
Example 3 Constructing a Truth Table for (p
q)
T
F
F
T
F
T
F
T
By tradition, this is always the way that truth
tables begin.
8
Example 4 Constructing a Truth Table for p V q
F
F
T
T
T
T
T
T
Note the two columns have the same truth values.
This equivalency is one of the De Morgan laws.
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De Morgan

• Great fleas have little fleas upon their backs to
  bite 'em,And little fleas have lesser fleas, and
  so ad infinitum.And the great fleas themselves,
  in turn, have greater fleas to go onWhile these
  again have greater still, and greater still, and
  so on.A Budget of Paradoxes.

10
Example 6 Constructing a Truth Table for (p V
q) q
T
F
F
F
T
F
T
T
Join these two columns with OR.
Join these two columns with AND.
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Exercise Set 3.3 1 - 4

• The Beatles were a rock group and Ernest
  Hemingway was a writer.
• John Travolta is an actor and Abraham Lincoln was
  a U.S. president.
• 3 2 5 and 3 is an even number.
• 7(5) 35 and 6 is an odd number.

T
T, T
T
T, T
F
T, F
F
T, F
12
Exercise Set 3.3 9 12

• Some athletes are not college professors or Sammy
  Sosa was a U.S. president.
• London is the capital of France or some students
  are not psychology majors.
• All politicians have law degrees or no students
  are business majors.
• All computers cost more than 1000 or no colleges
  have athletic programs

T
T, F
T
F, T
F
F, F
F
F, F
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Exercise Set 3.3 19 p q
F
F
F
T
14
Exercise Set 3.3 29 (p V q) (p V q)
T
F
F
T
F
F
T
F
F
T
F
F
Join these two columns with AND.
Join these two columns with OR.
AND.
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Homework Section 3.3

• Do 1-36