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 :

Correct Answer: (A) 1 only

Premise I states $P$$\implies$ (Q \land S) and Premise II states $(R \land S)$$\implies$ \neg T. For Conclusion 1: If T is true, the contrapositive of Premise II requires $\neg(R \land S)$$\iff$ (\neg R \lor \neg S). If R is false, then at least one of P and R is false. If R is true, then S must be false; by the contrapositive of Premise I ($\neg S$$\implies$ \neg P), P must be false. Thus, if T is true, at least one of P and R must be false (Conclusion 1 is valid). Conclusion 2 asserts $Q$$\implies$ P, which is the fallacy of affirming the consequent and does not follow.