1. Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.
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2. Chapter 3: Introduction to Logic
3.1 Statements and Quantifiers 3.2 Truth Tables and Equivalent Statements 3.3 The Conditional and Circuits 3.4 More on the Conditional 3.5 Analyzing Arguments with Euler Diagrams 3.6 Analyzing Arguments with Truth Tables
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3. Section 3-3 Chapter 1 The Conditional and Circuits
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4. The Conditional and Circuits
Conditionals
Negation of a Conditional
Circuits
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Conditionals
A conditional statement is a compound statement that uses the connective if…then.
The conditional is written with an arrow, so “if p then q” is symbolized
We read the above as “p implies q” or “if p then q.” The statement p is the antecedent, while q is the consequent.
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6. Truth Table for The Conditional, If p, then q
p q
T T T
T F F
F T
F F
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7. Special Characteristics of Conditional Statements
is false only when the antecedent is true and the consequent is false.
If the antecedent is false, then is automatically true.
If the consequent is true, then is automatically true.
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8. Example: Determining Whether a Conditional Is True or False
Decide whether each statement is True or False (T represents a true statement, F a false statement).
Solution
a) False
b) True
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Tautology
A statement that is always true, no matter what the truth values of the components, is called a tautology. They may be checked by forming truth tables.
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10. Negation of a Conditional
The negation of
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11. Writing a Conditional as an “or” Statement
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12. Example: Determining Negations
Determine the negation of each statement.
a) If you ask him, he will come.
b) All dogs love bones.
Solution
a) You ask him and he will not come.
b) It is a dog and it does not love bones.
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Circuits
Logic can be used to design electrical circuits. p p q
Series circuit q
Parallel circuit
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14. Equivalent Statements Used to Simplify Circuits
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15. Equivalent Statements Used to Simplify Circuits
If T represents any true statement and F represents any false statement, then
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16. Example: Drawing a Circuit for a Conditional Statement
Draw a circuit for
Solution
~ p q
~ r
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