Syllogism – Subset and existence reasoning Premises: 1) All aeroplanes are trains. 2) Some trains are chairs. Conclusions to test: I) Some aeroplanes are chairs. II) Some chairs are aeroplanes. III) Some chairs are trains. IV) Some trains are aeroplanes.

Introduction / Context:This problem blends a universal inclusion with a particular statement and asks which “some” conclusions are guaranteed. We must respect what is asserted and avoid assuming an intersection that is not given by the premises.

Given Data / Assumptions:

• A = aeroplanes, T = trains, C = chairs.
• Premise 1: All A are T (A ⊆ T).
• Premise 2: Some T are C (there exists at least one element in T ∩ C).
• Typical test convention assumes existence of A (at least one aeroplane).

Concept / Approach:From Premise 2, we know there is at least one chair that is a train, so “Some chairs are trains” is certain. From Premise 1 and the usual existence assumption, at least one train is an aeroplane, so “Some trains are aeroplanes” follows. However, there is no premise that connects A directly with C; thus we cannot say some aeroplanes are chairs, nor some chairs are aeroplanes.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Common Pitfalls:

Final Answer:Only III and IV follow