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 |

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| |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] |

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| |p |

| |q |

| |[pic] |

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| |T |

| |T |

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| |T |

| |T |

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| |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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