In a truth-conditional relation, if statement A being true guarantees that statement B is true, what is this relation called?

• A. A entails B
• B. A implies B
• C. They are contradictory
• D. B entails A

Answer: (A)

Entailment is the relation where the truth of one statement guarantees the truth of another. If A being true guarantees B, then B follows from A in every case, which is exactly what A entails B. The term implies a strong logical consequence: whenever A holds, B must hold as well.

The other phrasing like “A implies B” is a common way to talk about a conditional, but it’s a weaker, more flexible notion and doesn’t always carry the guarantee across all scenarios the way entailment does. The idea that they are contradictory would mean they cannot both be true, which isn’t the case when A guarantees B. The idea that B entails A is the reverse of the situation described, so it also doesn’t match.