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
Explanation :
Given main statement: Pradeep becomes either a Director or a Producer
Let’s define:
D = Pradeep is a Director
P = Pradeep is a Producer
R = Not Director
S = Not Producer
Analyzing statement pairs:
1. S implies P:
– If S is true (Not Producer)
– From main statement (must be Director or Producer)
– Then D must be true (Director)
This is valid
2. R implies Q:
– If R is true (Not Director)
– From main statement (must be Director or Producer)
– Then P must be true (Producer)
This is valid
Both pairs are logically valid based on the main statement that Pradeep must be either Director or Producer.
Answer: c) Both SP and RQ are valid implications.
