2024 CSAT — Q74

Locate. The “anchor” of a disjunction-consistency item is the connective in the main statement. Read it precisely: “either becomes a director or a producer” — a disjunction that guarantees at least one of the two roles. Everything else is testing each ordered pair against this one logical fact.

Test (disjunctive syllogism + direction check). For each pair, ask two things in order: (i) does the first statement imply the second? and (ii) are both consistent with the main statement? Pair SP: first is S = “not a producer.” Under the disjunction, denying one disjunct forces the other — not a producer ⇒ director. So S implies P, and both sit inside the disjunction. Valid. Pair RQ: first is R = “not a director.” Denying that disjunct forces the other — not a director ⇒ producer. So R implies Q, both consistent. Valid. Two valid pairs ⇒ both.

Eliminate by anatomy. (a) “Only SP” and (b) “Only RQ” are each half right, half wrong — they spot one valid disjunctive syllogism and stop, missing that the symmetric denial works on the other disjunct identically. (d) “Neither” gets the direction backwards — it fires when a reader checks implication in the wrong direction (e.g. asks whether P implies S) and finds it fails, not realising the pairs are written first-implies-second the correct way. The transferable move on a disjunction: denying either disjunct forces the other — so both “not-A ⇒ B” and “not-B ⇒ A” hold. Key: (c).

Main statement: “Pradeep either becomes a director or a producer” — a disjunction, so at least one of {director, producer} holds. Pair SP: S = “not a producer”; given the disjunction, if he is not a producer he MUST be a director, so S implies P — and both fit the main statement. Pair RQ: R = “not a director”; if not a director he MUST be a producer, so R implies Q — and both fit the main statement. Both ordered pairs are valid disjunctive syllogisms consistent with the main statement → (c).

The main statement is a disjunction: Pradeep is a director OR a producer (at least one holds).

Pair SP (S then P): S says Pradeep is not a producer. By disjunctive syllogism, if he is not a producer, the disjunction forces him to be a director — that is exactly P. So S implies P, and “not a producer, and a director” is fully consistent with “director or producer.” Pair SP is valid.

Pair RQ (R then Q): R says Pradeep is not a director. By the same syllogism, not a director forces producer — that is Q. So R implies Q, and “not a director, and a producer” is consistent with the main statement. Pair RQ is valid.

Both ordered pairs satisfy first-implies-second and are consistent with the disjunction. Answer: (c) Both SP and RQ.

The whole item turns on one logical fact most aspirants under-use: in a disjunction “A or B,” denying either disjunct forces the other. That symmetry is why both ordered pairs work — SP denies the producer and gets the director; RQ denies the director and gets the producer. The trap options each see only one half of that symmetry. The discipline that scores: read the connective, apply disjunctive syllogism in the stated direction (first implies second), and expect the symmetric pair to be equally valid.