Statements: • All desks are chairs. • All chairs are tables. • All tables are boxes. • All boxes are trunks. Conclusions: I. Some trunks are tables. II. All chairs are boxes. III. Some boxes are desks. IV. All desks are trunks. Choose the option that must follow.

Introduction / Context:Pure subset chains allow safe transitive conclusions with universals, but do not create existence. Therefore, “some” conclusions require caution unless an existential premise is present.

Given Data / Assumptions:Desks ⊆ Chairs ⊆ Tables ⊆ Boxes ⊆ Trunks.

Concept / Approach:From the chain, any Chair is a Box (II true), and any Desk is a Trunk (IV true). However, “Some trunks are tables” and “Some boxes are desks” assert existence of Tables and Desks, which the premises do not provide.

Step-by-Step Solution:• II: Chairs ⊆ Boxes by transitivity; universally true.• IV: Desks ⊆ Trunks by transitivity; universally true.• I: “Some trunks are tables” needs at least one Table; existence is not implied by the universals.• III: “Some boxes are desks” needs existence of a Desk; also not implied.

Verification / Alternative check:Let all sets be empty; the universals remain true, yet I and III are false due to lack of witnesses.

Why Other Options Are Wrong:They include existential claims not guaranteed by the premises.

Common Pitfalls:Confusing universals with existence claims.

Final Answer:Only II and IV follow.