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.
Correct Answer: Only III and IV follow
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:
Conclusion III: “Some chairs are trains.” True by Premise 2.Conclusion IV: “Some trains are aeroplanes.” If any aeroplane exists, it is a train; hence at least one train is an aeroplane.Conclusions I and II would require A ∩ C ≠ ∅, which is not given.Verification / Alternative check:
Construct a Venn diagram: place A entirely inside T; place C overlapping with part of T away from A. This satisfies both premises while making I and II false—showing they do not necessarily follow.Why Other Options Are Wrong:
A, B, C: Each accepts at least one of I or II which are not compelled.D correctly selects III and IV, the only necessary consequences.Common Pitfalls:
Assuming overlaps between subsets without explicit support; confusing “some T are C” with “some A are C.”Final Answer:Only III and IV follow