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:
Answer & explanation
Answer: (a) 1 only
If P and R were both true, P would make S true, and R with S would make T false. So whenever T is true, P or R must be false. 'If Q is true, then P is true' merely reverses statement I, which never follows.
- Test Conclusion 1: suppose T is true while P and R are both true.
- By I, P true makes Q and S true; so R and S are both true.
- By II, R and S true makes T false — contradicting T true. So Conclusion 1 follows.
- Test Conclusion 2: take Q true, P false (S, R, T anything consistent). Statement I is not violated, since it says nothing when P is false.
- So Q can be true without P; Conclusion 2 does not follow.
- ✓ 1. P and R both true would force S true and then T false; so with T true, P or R must be false.
- ✗ 2. It is the converse of statement I; Q can be true while P is false.
Remember · 'If A then B' gives 'if not B then not A', never 'if B then A'. Test a conclusion by assuming it fails.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·