Syllogism – Some + No relation: Statements: (a) Some skirts are benches. (b) No bench is a table. Conclusions: I) Some skirts are tables. II) Some benches are skirts. III) All benches are skirts. IV) Some tables are skirts.

Introduction / Context:We combine one particular overlap with a universal exclusion to test which conclusions are necessary.

Given Data / Assumptions:

• Some Skirts are Benches (∃ S ∩ B).
• No Bench is a Table (B ∩ T = ∅).

Concept / Approach:Conclusion II restates the given particular in symmetric form and must hold. Conclusions I and IV claim a Skirt–Table overlap, which is not supported and in fact contradicted for the bench-portion of skirts by the “No bench is a table” clause. Conclusion III (“All benches are skirts”) is stronger than the “some” premise and is not compelled.

Step-by-Step Solution:From ∃ S ∩ B, we can assert “Some benches are skirts” (II).Because B ∩ T = ∅, any element of B is not in T; therefore the overlap cannot imply any Skirt–Table overlap.

Verification / Alternative check:Model: Let a few benches be skirts; keep tables disjoint from benches. The premises hold; II holds; I, III, IV do not necessarily follow.

Why Other Options Are Wrong:They claim overlaps that are not guaranteed or universally quantify from a “some”.

Common Pitfalls:Illicit conversion and over-generalizing from an existential.

Final Answer:Only II follows.