Deductive versus Inductive Reasoning
Truth Tables
|Objectives: | |
|Construct a truth table for a given symbolic expression. | |
|Determine if two given statements are equivalent using truth tables. | |
|Use De Morgan’s Laws to write a statement equivalent to a given statement. | |
|Vocabulary: |Negation |
|truth table | |
|equivalent expressions |Conjunction |
|De Morgan’s Laws | |
| |p |
| |~p |
| | |
| |p |
| |q |
| |[pic] |
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| |T |
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| |T |
| |T |
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| |F |
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| |T |
| |F |
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| |F |
| |T |
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| |F |
| |F |
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| |Disjunction |
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| |Conditional |
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| |p |
| |q |
| |[pic] |
| | |
| |p |
| |q |
| |[pic] |
| | |
| |T |
| |T |
| | |
| | |
| |T |
| |T |
| | |
| | |
| |T |
| |F |
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| |T |
| |F |
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| |F |
| |T |
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| |F |
| |T |
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| |F |
| |F |
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| |F |
| |F |
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|Complete the negations of the basic connectives: |
|[pic] |
|[pic] |
|[pic] |
|[pic] |
Possible Classroom Examples:
• Construct a truth table for [pic]
|p |~p |[pic] |
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| | | |
• Construct a truth table for [pic]
|p |q |[pic] |~q |[pic] |
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• Construct a truth table for the following statement:
If the lyrics are not controversial, then performance is not banned.
p:
q:
symbolic form:
|p |q | | | |
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• Construct a truth table for the following statement:
The country singer is in trouble if he is elected.
p:
q:
symbolic form:
|p |q | | | |
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• Construct a truth table for the following statement:
If he does not go to jail, he is innocent or has an alibi.
p:
q:
r:
symbolic form:
|p |q |r | | |
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• Construct a truth table for [pic]
|p |q | | | |
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• Construct a truth table to determine whether the following statements are equivalent:
The streets are wet or it is not raining.
If it is raining, then the streets are wet.
p:
q:
|symbolic form: |symbolic form: |
|p |p |
|q |q |
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