Introduction / Context:
This item requires careful separation of what is guaranteed versus what is merely possible. We chain subsets and one existential statement to test each conclusion.
Given Data / Assumptions:
- All Benches are Desks (B ⊆ D).
- Some Desks are Roads (∃ D ∩ R).
- All Roads are Pillars (R ⊆ P).
Concept / Approach:
- From ∃(D ∩ R) and R ⊆ P, it follows that ∃(D ∩ P): some Pillars are Desks.
- No information forces any Bench to be a Road; Benches are a subset of Desks but need not participate in the Desks∩Roads region.
Step-by-Step Solution:
(II) “Some pillars are desks” necessarily follows: take the “Some Desks are Roads,” then map Roads into Pillars, yielding Desks that are also Pillars.(I) “Some pillars are benches” is not compelled; the Desks that are Roads (hence Pillars) could be entirely outside the Benches subset of Desks.(III) “Some roads are benches” is likewise not necessary; the roads that intersect desks need not intersect the benches portion of desks.(IV) “No pillar is a bench” is a universal negative not supported; pillars could include some benches if the “desk-road” overlap happened to lie within benches, but this is not guaranteed.
Verification / Alternative check:
Create a model where Benches are a small part of Desks, and the Desks∩Roads area lies away from Benches. All premises hold; (II) true; (I), (III), (IV) false. Hence only (II) must be true.
Why Other Options Are Wrong:
Any choice adding (I), (III), or (IV) asserts overlaps or disjointness not mandated by the premises. “All follow” is clearly too strong.
Common Pitfalls:
Assuming subset membership (B ⊆ D) forces benches into every region where desks appear. That is invalid.
Final Answer:
Only II follows
Discussion & Comments