3'3 Truth Table for negation, conjunction, disjunction p' 103112 3'4 Truth Tables for the Conditiona

1
3.3 Truth Table for negation, conjunction,
disjunction p. 103-1123.4 Truth Tables for the
Conditional and Biconditional p. 115-123

• OBJECTIVES
• Use the definition of negation, conjunction,
  disjunction
• Use DeMorgans Law
• Use definitions of conditional and its variations

2
Compound Statements, 94
Simple statements can be connected with and,
Either or, If then, or if and only if.
These more complicated statements are called
compound. Examples Miami is a city in
Florida is a true statement. Atlanta is a city
in Florida is a false statement. Either Miami
is a city in Florida or Atlanta is a city in
Florida is a compound statement that is
true. Miami is a city in Florida and Atlanta is
a city in Florida is a compound statement that
is false.
3
And Statements, p. 95

• When two statements are represented by p and q
  the compound and statement is p /\ q.
• p Harvard is a college.
• q Disney World is a college.
• p/\q Harvard is a college and Disney World is a
  college.
• p/\q Harvard is a college and Disney World is
  not a college.

4
Either ... or Statements, p. 96

• When two statements are represented by p and q
  the compound Either ... or statement is p\/q.
• p The bill receives majority approval.
• q The bill becomes a law.
• p\/q The bill receives majority approval or the
  bill becomes a law.
• p\/ q The bill receives majority approval or
  the bill does not become a law.

5
If ... then Statements, p. 96

• When two statements are represented by p and q
  the compound If ... then statement is p ? q.
• p Ed is a poet.
• q Ed is a writer.
• p ? q If Ed is a poet, then Ed is a writer.
• q ? p If Ed is a writer, then Ed is a poet.
• q ? p If Ed is not a writer, then Ed is not a
  Poet

6
If and only if Statements, p.98

• When two statements are represented by p and q
  the compound if and only if statement is
  p ? q.
• p The word is set.
• q The word has 464 meanings.
• p ? q The word is set if and only if the word
  has 464 meanings.
• q ? p The word does not have 464 meanings if
  and only if the word is not set.

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Symbolic Logic, p. 99

• Statements of Logic
• Name Symbolic Form
• Negation p
• Conjunction p/\q
• Disjunction p\/q
• Conditional p ? q
• Biconditional p? q

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Truth Tables Negation, p. 103
If a statement is true then its negation is
false. If the statement is false then its
negation is true. This can be represented in the
form of a table called a truth table.
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Truth Tables Conjunction, p.104
The conjunction of two statements is true only
when both of them are true.
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Truth Tables Disjunction, p.106
The disjunction of two statements is false only
when both of them are false.
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Constructing a Truth Table, p. 107

• Construct a truth table for ((p/\q)\/q).

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Truth Tables Conditional, p. 116
A conditional statement is false only when the
antecedent (the if part) is true and the
consequent (the then part) is false.

13
Truth Tables Biconditional, p. 120
A biconditional statement is true whenever the
antecedent (the if part) and the consequent
(the then part) are both true or both false.

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Tautology, p. 118
A tautology is a statement that is always true.


15
Equivalent Statements, p. 127
Two statements are equivalent if they have the
same truth values.


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HOMEWORK

• P. 101-102 1-61 alt odd, Critical Thinking 76,77
• 113-115 1-36 alt odd, Critical Thinking 60-62
• Read p. 126-145
• PRE QUIZ (3.5, 3.6)
• Office hours M-F 900-1015
• or by appointment