2021 CSAT — Q49

Locate. This is a pure-logic question (no passage): the given premise set is the anchor, and a conclusion follows only if the premises make it impossible to be false. Render: Greens overlap Blues (some), Blues overlap Blacks (some). Both links are particular, and they share only the middle term Blues.

Test (does-it-follow — build counter-models). The green-black relation is entirely open because two unanchored “some” overlaps cannot pin it down.

• C-1 “some greens are blacks” — counter-model: let the green-blues and the black-blues be separate parts of Blues; then no green is black. Not forced.
• C-2 “no green is black” — counter-model: let those parts overlap; then some green is black. Not forced.
• C-3 “all greens are blacks” — two particulars never force a universal. Not forced.
• C-4 “all blacks are greens” — likewise unforced (and the link is the wrong direction anyway). Not forced.

Eliminate by anatomy. (a) pairs C-1 and C-2 — but they are contradictory (some-are vs none-are), so they cannot both follow; this is the trap of mistaking a complementary either/or for a conjunction — it sounds reasonable, but is unsupported. (b)/(c) assert universals (C-3, C-4) that two particulars cannot yield. Since no single conclusion holds in every model, the answer is (d) none follows.

Premises: Greens ∩ Blues ≠ ∅; Blues ∩ Blacks ≠ ∅. The green–black link runs through TWO unanchored “some” overlaps, so it is wholly undetermined. C-1 “some greens are blacks” — counter-model: the green-blues and the black-blues are disjoint slices of Blues, so no green is black → not forced. C-2 “no green is black” — counter-model: those slices overlap, so some green is black → not forced. C-3 “all greens are blacks” and C-4 “all blacks are greens” — neither is forced by two particulars. NO single conclusion holds in every model → (d). (C-1 and C-2 are a complementary either/or pair, but option (a) asserts BOTH, which is impossible; no option offers the legitimate “either-or,” so none individually follows.)

Premises: Greens ∩ Blues ≠ ∅; Blues ∩ Blacks ≠ ∅.

• C-1 — counter-model with disjoint blue-slices refutes necessity. Does not follow.
• C-2 — counter-model with overlapping blue-slices refutes necessity. Does not follow.
• C-3 / C-4 — universals unforced by two “some” premises. Do not follow.

C-1 and C-2 form a complementary pair (exactly one is true in any given model), so their either/or would follow — but no option offers “either C-1 or C-2,” and (a) wrongly asserts both at once. With no single conclusion necessary, the verdict is none.

Answer: (d) Neither Conclusion 1 nor 2 nor 3 nor 4.

Two traps live here. First, the complementary-pair trap: C-1 (“some are”) and C-2 (“none are”) are exact opposites, so in any single model exactly one is true — which tempts a student to tick “C-1 and C-2.” But “exactly one of them is true” is not “both follow”; their either/or follows, their conjunction never can. Since no option offers the either/or and (a) demands both, (a) is wrong. Second, the universal trap: two “some” premises can never deliver an “all.” With every individual conclusion refutable by a counter-model, the disciplined verdict is “none follows.” (d).