Question

Which one of the following is NOT a true statement about the relation between logical equivalence and entailment?

A) Contradictions entail all other formulas.
B) Tautologies entail other tautologies.
C) If formula 'a' entails formula 'b', then on a table.
D) Every tautology contains at least one repeated sentence letter.

Answer 1

The correct answer is C) If formula 'a' entails formula 'b', then on a table.

Step-by-step explanation:

The correct answer is C) If formula 'a' entails formula 'b', then on a table.

Logical equivalence is a relation between two formulas where one formula is true if and only if the other formula is true. Entailment is a relation between two formulas where if formula 'a' entails formula 'b', then every truth assignment that makes 'a' true also makes 'b' true.

In option C, it states that if formula 'a' entails formula 'b', then on a table. This statement is not true because entailment holds for every possible truth assignment and is not limited to just a table.

Contradictions entail all other formulas (option A) and tautologies entail other tautologies (option B). Every tautology contains at least one repeated sentence letter (option D).