Syllogism — Nested inclusions and an external existential Statements: • All chairs are tables. • All tables are cushions. • Some cushions are trolleys. • All trolleys are lamps. Conclusions: I) Some lamps are tables. II) Some trolleys are chairs. III) Some cushions are lamps. IV) All chairs are cushions. Choose the correct set.

Introduction / Context:
Nesting inclusions allow some conclusions to be read off immediately, while an existential about another branch creates a separate chain. The trick is to avoid assuming intersections that are not enforced.

Given Data / Assumptions:

• Chairs ⊆ Tables.
• Tables ⊆ Cushions.
• ∃t: t ∈ Cushions ∩ Trolleys.
• Trolleys ⊆ Lamps.

Concept / Approach:
From Chairs ⊆ Tables ⊆ Cushions, it follows that All chairs are cushions (IV). The existential witness t in Cushions ∩ Trolleys, combined with Trolleys ⊆ Lamps, implies that Some cushions are lamps (III). However, to claim “Some lamps are tables” or “Some trolleys are chairs” would require the trolley witness to lie inside Tables/Chairs, which is not guaranteed.

Step-by-Step Solution:

Verification / Alternative check:
Diagram two branches: (Chairs → Tables → Cushions) and (Cushions ← Trolleys → Lamps). The trolley branch meets Cushions but need not pass through Tables/Chairs.

Why Other Options Are Wrong:
They assume overlaps between Trolleys and Tables/Chairs that the premises do not create.

Common Pitfalls:
Overextending an existential witness into unrelated subsets merely because they share a common superset.

Final Answer:
Only III and IV follow.