2021 CSAT — Q15

Locate. This is a pure-logic question (no passage) — the premise set is the anchor. Render it: Cats overlap Almirahs; Almirahs overlap Chairs; All Chairs are Tables (Chairs ⊆ Tables).

Test (does-it-follow, per conclusion).

• C-I “Certainly some almirahs are tables” — the overlap “some almirahs are chairs” gives at least one almirah-chair; every chair is a table; so that almirah is a table. Forced — follows.
• C-II “Some cats may not be chairs” — this is a possibility statement. The cat–chair link runs only through two unanchored “some” overlaps (cats∩almirahs, almirahs∩chairs), so nothing fixes whether any cat is a chair. Because “some cats are not chairs” is possible (a counter-model where no cat is a chair satisfies every premise), the possibility-conclusion rule licenses “some cats may not be chairs.” Follows (possibility read).

Eliminate by anatomy. (d) wrongly drops the forced C-I. (b) wrongly drops C-I. The live contest is (c) vs (a), and it is purely a reading convention for “may not” (possibility-operator vs hedged-definite) — see the contest box below. Blind key on the possibility rule: (c).

Premises: Cats ∩ Almirahs ≠ ∅; Almirahs ∩ Chairs ≠ ∅; Chairs ⊆ Tables. C-I “Certainly some almirahs are tables” is FORCED: the almirahs that are chairs are tables (Chairs ⊆ Tables), so some almirahs are tables. C-II “Some cats may not be chairs” is a POSSIBILITY claim; the cat–chair relation is wholly undetermined (two unanchored “some” links), so “some cats are not chairs” is possible → under the standard possibility-conclusion rule, C-II also follows → blind (c). Contest: UPSC’s official key is (a) Only Conclusion-I — it rejects C-II, reading “may not” as a definite “are not” (which is indeed not forced). Both keys turn on the convention for reading “may not”; dual-shown, excluded from scoring.

Premises: Cats ∩ Almirahs ≠ ∅; Almirahs ∩ Chairs ≠ ∅; Chairs ⊆ Tables.

• C-I — an almirah that is a chair is a table (chairs are tables), so some almirahs are tables. Definitely follows.
• C-II — “some cats may not be chairs” asserts only the possibility that some cats fall outside chairs. Since the cat–chair relation is undetermined, that possibility genuinely exists; a possibility conclusion follows when it is not impossible. Follows on the possibility convention.

Blind answer: (c) Both — under the rule that a “may/may not” conclusion follows whenever the relation is undetermined.

The honest crux is a notation convention, not a reasoning slip. C-I is forced beyond dispute. C-II hangs entirely on how “may not” is read: as a possibility operator (“it is possible that some cats are not chairs” — true, since the relation is open) it follows, giving (c); as a hedged definite (“some cats are not chairs” with a softening “may”) it does not follow, giving (a). UPSC’s key takes the second reading. Because a defensible deduction supports each key depending on a convention the stem does not pin down, we dual-show both keys and exclude the item from scoring rather than bend the deduction to the official letter. This is precisely the free-CR fuzziness the founder spot-check exists to arbitrate.