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 ✓ UPSC's answer
- (d) Neither SP nor RQ
Why the answer is (c)
["- The Main Statement 'Pradeep becomes either a Director or a Producer' establishes an exclusive or inclusive disjunction where exactly one of the two roles is held, or at least one is held, but in logical implication contexts for such questions, it typically implies a binary choice where if one is false, the other must be true.", "- Consider the pair SP: Statement S is 'Pradeep is not a Producer'. If S is true, then based on the Main Statement, Pradeep must be a Director. Therefore, S implies P ('Pradeep is a Director').", "- Consider the pair RQ: Statement R is 'Pradeep is not a Director'. If R is true, then based on the Main Statement, Pradeep must be a Producer. Therefore, R implies Q ('Pradeep is a Producer').", '- Both pairs (S implying P) and (R implying Q) are logically consistent with the Main Statement because the negation of one role necessitates the other role in this binary scenario.', '- Since both SP and RQ satisfy the condition that the first statement implies the second and are consistent with the main statement, the correct option is (c).']
Why the other options are wrong
- (a) SP only
- Option (a) is incorrect because it excludes the valid pair RQ, where 'Pradeep is not a Director' logically implies 'Pradeep is a Producer'.
- (b) RQ only
- Option (b) is incorrect because it excludes the valid pair SP, where 'Pradeep is not a Producer' logically implies 'Pradeep is a Director'.
- (d) Neither SP nor RQ
- Option (d) is incorrect because both pairs SP and RQ are logically valid implications derived from the Main Statement.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.