Deck 3: Truth Tables

Question 1

General Theory

-Determine the sentence forms of which the following are substitution instances:
a.
b.

Answer 1

a.
b.

Question 2

General Theory
-If a sentence form contains five variables, how many lines or rows must its complete truth table analysis have?

Answer 2

There would be $2^{5} = 32$ rows of the truth table.

Question 3

General Theory
-Assume you know of an argument only that its premises are not consistent. What, if anything, can you tell about the argument's validity? (Defend your answer.)

Answer 3

If an argument's premises are not consistent then it will be impossible for all of them to be true. Therefore, the argument must be valid, because it will be impossible for the premises to be true and the conclusion false.

Question 4

General Theory
-Why is it true that any argument with a conclusion with the form $p \vee \thicksim p$ is valid?

Question 5

General Theory
-a. We can define a tautologous sentence as one that is a substitution instance of some tautologous sentence form, and a contradictory sentence as one that is a substitution instance of some contradictory sentence form. Why can't we analogously define a contingent sentence as one that is a substitution instance of some contingent sentence form? (Defend your answer, including examples.)
b. We cannot define a contingent sentence as one that is a substitution instance of some contingent sentence form. But then how can we define that term?

Question 6

General Theory
-Suppose one of the premises of an argument is logic equivalent to the conclusion. What, if anything, can you conclude about the argument's validity?

Question 7

Tautologies, Contradictions, and Contingent Sentences
Determine by truth table analysis which of the following sentence forms are tautologous, which are contradictory, and which are contingent:
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Question 8

Tautologies, Contradictions, and Contingent Sentences
Determine by truth table analysis which of the following sentence forms are tautologous, which are contradictory, and which are contingent:
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Question 9

Tautologies, Contradictions, and Contingent Sentences
Determine by truth table analysis which of the following sentence forms are tautologous, which are contradictory, and which are contingent:
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Question 10

Tautologies, Contradictions, and Contingent Sentences
Determine by truth table analysis which of the following sentence forms are tautologous, which are contradictory, and which are contingent:
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Question 11

Tautologies, Contradictions, and Contingent Sentences
Determine by truth table analysis which of the following sentence forms are tautologous, which are contradictory, and which are contingent:
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Question 12

Logical Equivalences
Use a truth table to determine which of the following pairs of sentence forms are logically equivalent.
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Question 13

Logical Equivalences
Use a truth table to determine which of the following pairs of sentence forms are logically equivalent.
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Question 14

Logical Equivalences
Use a truth table to determine which of the following pairs of sentence forms are logically equivalent.
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Question 15

Logical Equivalences
Use a truth table to determine which of the following pairs of sentence forms are logically equivalent.
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Question 16

Proving Validity of Argument Forms
Determine by truth table analysis which of the following argument forms are valid and which are invalid:
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Question 17

Proving Validity of Argument Forms
Determine by truth table analysis which of the following argument forms are valid and which are invalid:
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Question 18

Proving Validity of Argument Forms
Determine by truth table analysis which of the following argument forms are valid and which are invalid:
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Question 19

Proving Validity of Argument Forms
Determine by truth table analysis which of the following argument forms are valid and which are invalid:
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Question 20

Short Truth Table Test for Invalidity
Use the short truth table method to show that the following arguments are invalid:
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Question 21

Short Truth Table Test for Invalidity
Use the short truth table method to show that the following arguments are invalid:
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Question 22

Short Truth Table Test for Invalidity
Use the short truth table method to show that the following arguments are invalid:
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Question 23

Short Truth Table Test for Invalidity
Use the short truth table method to show that the following arguments are invalid:
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Question 24

Short Truth Table Test for Consistency
Use the short truth table method to show that the following sets of premises are consistent:

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Question 25

Short Truth Table Test for Consistency
Use the short truth table method to show that the following sets of premises are consistent:

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Question 26

Short Truth Table Test for Consistency
Use the short truth table method to show that the following sets of premises are consistent:

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Question 27

Short Truth Table Test for Consistency
Use the short truth table method to show that the following sets of premises are consistent:

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