Let P, Q, R, S and T be five statements such that: I. If P is true, then both Q and S are true. II. If R and S are true, then T is false. Which of the following can be concluded? 1. If T is true, then at least one of P and R must be false. 2. If Q is true, then P is true. Select the correct answer…

Question

Let P, Q, R, S and T be five statements such that: I. If P is true, then both Q and S are true. II. If R and S are true, then T is false. Which of the following can be concluded? 1. If T is true, then at least one of P and R must be false. 2. If Q is true, then P is true. Select the correct answer using the code given below:

Aicharya · Accepted Answer

Conclusion 1: Suppose T is true. From rule II, 'R and S true implies T false', so if T is true, not both R and S are true; hence R is false or S is false. If S is false, then by rule I (P implies Q and S), P cannot be true. Thus T true implies at least one of P and R is false. Conclusion 1 follows. Conclusion 2: Q being true does not imply P is true (the implication is one-directional). Conclusion 2 does not follow. Only conclusion 1.

Let P, Q, R, S and T be five statements such that: I. If P is true, then both Q and S are true. II. If R and…

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