Statements: All benches are desks. Some desks are roads. All roads are…
2024
Statements: All benches are desks. Some desks are roads. All roads are pillars.
Conclusions:
I. Some pillars are benches.
II. Some pillars are desks.
III. Some roads are benches.
IV. No pillar is bench.
- A.
Only either I or IV follows
- B.
Only either I or IV, and II follow
- C.
None follows
- D.
All follows
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Correct answer: B
Concept: In syllogism, a conclusion between the two extreme terms follows only if the shared middle term is distributed in at least one of the two premises being combined. If neither premise distributes the middle term, no direct conclusion follows between the extremes -- unless the two candidate conclusions about those same two terms form a complementary ('some' / 'no') pair, in which case exactly one of that pair must be true, giving an Either...Or result. Any valid 'Some A are B' conclusion also converts validly to 'Some B are A'.
All benches are desks (universal) and Some desks are roads (particular): the middle term 'desks' is undistributed in both premises, so no definite conclusion links benches and roads -- 'Some roads are benches' does not follow.
Some desks are roads (particular) and All roads are pillars (universal): the middle term 'roads' is distributed in the universal premise, so a valid particular conclusion follows -- 'Some desks are pillars'.
Converting that particular conclusion validly gives 'Some pillars are desks', which matches one of the listed conclusions exactly.
Combining All benches are desks with the derived Some desks are pillars: the middle term 'desks' is again undistributed in both, so this chain alone gives no direct conclusion linking benches and pillars.
However, the two candidate conclusions relating pillars and benches ('some pillars are benches' and 'no pillar is bench') form a complementary pair about the same two terms, so exactly one of them must hold -- giving an Either-Or result between them.
Cross-check: two different valid class arrangements consistent with all three statements can be built -- one where 'no pillar is bench' holds, another where 'some pillars are benches' holds -- confirming that relationship is genuinely undecided between the two (hence Either-Or). In every such arrangement, however, the pillars-desks particular relationship holds without exception, confirming it is a fixed, definite result rather than an either-or case.
Result: the definite conclusion is the particular relationship between pillars and desks, together with an Either-Or between the two candidate pillars-benches relationships -- 'Some roads are benches' does not follow at all, since the benches-roads chain never distributes its middle term.