Exactly two of P, Q, R are true. If P and Q are true, what is R?

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Multiple Choice

Exactly two of P, Q, R are true. If P and Q are true, what is R?

This question tests what happens when there’s a fixed number of true statements among a small set. If exactly two of P, Q, R are true, then one of them must be false. If P and Q are true, that already accounts for two true statements. To keep the total at exactly two, R cannot be true. Therefore R must be false. If R were true as well, all three would be true, which contradicts the given condition. There’s no ambiguity here—the value of R is determined by the requirement that exactly two of the three are true.

This question tests what happens when there’s a fixed number of true statements among a small set. If exactly two of P, Q, R are true, then one of them must be false.

If P and Q are true, that already accounts for two true statements. To keep the total at exactly two, R cannot be true. Therefore R must be false. If R were true as well, all three would be true, which contradicts the given condition. There’s no ambiguity here—the value of R is determined by the requirement that exactly two of the three are true.

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