UPSC Prelims 2023 · CSAT

Question 78: Logical Reasoning and Mental Ability

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 :

a1 only

b2 only

cBoth 1 and 2

dNeither 1 nor 2

AnswerUPSC’s answer is (a).

The rules: P implies both Q and S; R and S together imply not T. Conclusion 1: suppose T is true and P and R are both true. P gives S true; then R and S true make T false, a contradiction. So when T is true, P and R cannot both be true, meaning at least one is false. Conclusion 2 reverses rule I: Q true does not force P true, which is the mistake of affirming the consequent.

1. If T, P and R were all true, P would force S, and R with S would force not T, a contradiction.
2. Rule I does not work backwards; Q can be true without P.

How you could have got this

If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: If T, P and R were all true, P would force S, and R with S would force not T, a contradiction.
Then, if you were sure statement 2 is not correct, (c) goes: it includes 2.
What you needed to know: Rule I does not work backwards; Q can be true without P.

Only (a) is left. This one needs every statement.

Which options go is worked out from UPSC’s key and the options, not by a model.

Why each option is right or wrong

(a) Right: only conclusion 1 follows.
(b) Wrong: conclusion 2 reverses rule I and does not follow.
(c) Wrong: conclusion 2 does not follow.
(d) Wrong: conclusion 1 follows.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.