If exactly two of P, Q, R are true and P is true while Q is false, what is R?

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Multiple Choice

If exactly two of P, Q, R are true and P is true while Q is false, what is R?

The key idea is that a fixed number of true statements among P, Q, and R forces the remaining value when some are known. Here, exactly two are true, and we know P is true while Q is false. To reach the total of two true statements, R must be true. If R were false, only P would be true, giving just one true, which contradicts the requirement. If R is true, the two true statements are P and R, satisfying the condition. Therefore, R must be true.

The key idea is that a fixed number of true statements among P, Q, and R forces the remaining value when some are known. Here, exactly two are true, and we know P is true while Q is false. To reach the total of two true statements, R must be true. If R were false, only P would be true, giving just one true, which contradicts the requirement. If R is true, the two true statements are P and R, satisfying the condition. Therefore, R must be true.

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