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: (C)

A biconditional is a statement that links two parts with the phrase “if and only if,” capturing a bidirectional relationship. It states that each part guarantees the other: if p is true, q is true, and if q is true, p is true. Equivalently, it’s true exactly when p and q have the same truth value, and it’s the same as saying p implies q and q implies p together. That makes the defining feature the presence of the phrase “if and only if.” It isn’t just two separate conditions or a conditional with a negation; it’s a single statement expressing that the two parts are true together in both directions.

A biconditional is a statement that links two parts with the phrase “if and only if,” capturing a bidirectional relationship. It states that each part guarantees the other: if p is true, q is true, and if q is true, p is true. Equivalently, it’s true exactly when p and q have the same truth value, and it’s the same as saying p implies q and q implies p together.

That makes the defining feature the presence of the phrase “if and only if.” It isn’t just two separate conditions or a conditional with a negation; it’s a single statement expressing that the two parts are true together in both directions.