Chapter 3

Question 1

Truth-functional truth

Answer 1

A sentence P of SL is truth-functionally true if and only if P is true on every truth-value assignment.

Question 2

Truth-functional falsity

Answer 2

A sentence P of SL is truth-functionally false if and only if P is false on every truth-value assignment.

Question 3

Truth-functional indeterminacy

Answer 3

A sentence P of SL is truth-functionally indeterminate if and only if P is neither truth-functionally true nor truth-functionally false.

Question 4

Truth-functional equivalence?

Answer 4

Sentences P and Q of SL are truth-functionally equivalent if and only if there is no truth-value assignment on which P and Qu have different truth-values.

Question 5

Truth-functional consistency

Answer 5

A set of sentences of SL is truth-functionally consistent if and only if there is at least one truth-value assignment on which all the members of the set are true. A set of sentences of SL is truth-functionally inconsistent if and only if the set is not truth-functionally consistent.

Question 6

Truth-Functional entailment

Answer 6

A set (GAMMA) of sentences of SL truth-functionally entails a sentence P of SL if and only if there is no true-value assignment on which every member of GAMMA is true and P is false.

Question 7

Truth-functional validity

Answer 7

An argument of SL is truth-functionally valid if and only if there is no truth-value assignment on which all the premises are true and the conclusion is false. An argument of SL is truth-functionally invalid if and only if it is not truth-functionally valid.