What does a biconditional statement express?

A biconditional statement expresses a relationship between two statements where both statements are either true or false, meaning that it is true if both statements have the same truth value. This is formally represented as "P if and only if Q," signifying that the truth of one statement depends on the truth of the other in such a way that they align completely.

To elaborate, if P and Q are both true, then the biconditional is true. Conversely, if both are false, the biconditional remains true. If one is true while the other is false, then the biconditional is false, showing that the truth values must match for the biconditional to hold. This core principle is what differentiates biconditional statements from other types of logical connectors that might only require one statement to imply the other or have varying truth conditions.

For clarity on why the other answers do not capture the essence of a biconditional statement: the implication of one statement by another does not require them to share truth values. Moreover, stating that both statements must be false does not represent a complete understanding, as a biconditional can also be true when both are true. Lastly, asserting that its truth is independent of the truth values oversimplifies