Which statement best defines a biconditional statement?

Which statement best defines a biconditional statement?

• A. A statement that contains the phrase 'if and only if'
• B. A statement that is always true
• C. A statement that has two independent conditions
• D. A conditional with a negation

Answer: (A)

A biconditional links two statements so that each implies the other, meaning they share the same truth value. This bidirectional relationship is exactly captured by the phrase “if and only if,” which is how a biconditional is commonly written (p if and only if q). So a statement that contains that phrase best defines a biconditional. In logic, such a statement is true when both parts are true or both are false, and false when one is true and the other false. The other ideas don’t fit because a biconditional isn’t about something that’s always true, nor is it merely two independent conditions joined together, nor is it just a conditional with negation.

A biconditional links two statements so that each implies the other, meaning they share the same truth value. This bidirectional relationship is exactly captured by the phrase “if and only if,” which is how a biconditional is commonly written (p if and only if q). So a statement that contains that phrase best defines a biconditional. In logic, such a statement is true when both parts are true or both are false, and false when one is true and the other false. The other ideas don’t fit because a biconditional isn’t about something that’s always true, nor is it merely two independent conditions joined together, nor is it just a conditional with negation.