Q. A Main Statement is followed by four Statements labelled P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement.
Main Statement: Pradeep becomes either a Director or a Producer.
Statement P: Pradeep is a Director
Statement Q: Pradeep is a Producer.
Statement R: Pradeep is not a Director.
Statement S: Pradeep is not a Producer.
Select the correct answer.
a) SP only
b) RQ only
c) Both SP and RQ
d) Neither SP nor RQ
Correct answer: c) Both SP and RQ
Question from UPSC Prelims 2024 CSAT Paper
Explanation:
Let’s analyze this step-by-step:
1. The Main Statement says that Pradeep becomes either a Director or a Producer. This means he can be one, but not both.
2. Now, let’s look at the implications between the statements:
P implies not Q (If Pradeep is a Director, he’s not a Producer)
Q implies not P (If Pradeep is a Producer, he’s not a Director)
R implies Q (If Pradeep is not a Director, he must be a Producer)
S implies P (If Pradeep is not a Producer, he must be a Director)
3. The question asks for an ordered pair where the first statement implies the second, and both are consistent with the Main Statement.
4. Let’s check the given options:
SP: S implies P, and both are consistent with the Main Statement.
RQ: R implies Q, and both are consistent with the Main Statement.
5. Both SP and RQ satisfy the conditions.
Therefore, the correct answer is c) Both SP and RQ.