If P ↔ Q is true, what does this say about P and Q?

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Multiple Choice

If P ↔ Q is true, what does this say about P and Q?

A biconditional is true exactly when the two propositions match in truth value. So if P ↔ Q is true, P and Q move together: when P is true, Q must be true; when P is false, Q must be false. In other words, they share the same truth value. That’s why the other ideas don’t fit: the statement doesn’t require P to be always true or Q to be always false, and it does not treat P and Q as unrelated. The given truth of the biconditional specifically enforces that P and Q have the same truth value.

A biconditional is true exactly when the two propositions match in truth value. So if P ↔ Q is true, P and Q move together: when P is true, Q must be true; when P is false, Q must be false. In other words, they share the same truth value.

That’s why the other ideas don’t fit: the statement doesn’t require P to be always true or Q to be always false, and it does not treat P and Q as unrelated. The given truth of the biconditional specifically enforces that P and Q have the same truth value.

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