If P and Q have the same truth value, P <-> Q is true.

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Multiple Choice

If P and Q have the same truth value, P <-> Q is true.

In logic, the biconditional P <-> Q is true exactly when P and Q have the same truth value. This means it’s true if both are true or both are false, and it’s false if one is true and the other is false. If both P and Q are true, P <-> Q is true because each side matches the other. If both are false, P <-> Q is still true: an implication with a false antecedent is true, so both directions (P implies Q and Q implies P) hold, making their conjunction true. When P and Q differ, the biconditional fails because the statements don’t match. So, when P and Q share the same truth value, P <-> Q is true.

In logic, the biconditional P <-> Q is true exactly when P and Q have the same truth value. This means it’s true if both are true or both are false, and it’s false if one is true and the other is false.

If both P and Q are true, P <-> Q is true because each side matches the other. If both are false, P <-> Q is still true: an implication with a false antecedent is true, so both directions (P implies Q and Q implies P) hold, making their conjunction true. When P and Q differ, the biconditional fails because the statements don’t match.

So, when P and Q share the same truth value, P <-> Q is true.

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