Syllogism — Shops, rooms, and kitchens (propagating “some” through a universal): Statements: • Some shops are rooms. • All rooms are kitchens. Conclusions: I. All shops are kitchens. II. Some shops are kitchens. III. Some rooms are shops. IV. All kitchens are shops.

Introduction / Context:We track an existential subset through a universal inclusion and also read the original overlap symmetrically.

Given Data / Assumptions:

• ∃ (Shop ∩ Room).
• Room ⊆ Kitchen.

Concept / Approach:The shops that are rooms are certainly kitchens, so II holds. The original premise “Some shops are rooms” is equivalent to “Some rooms are shops,” so III also holds. I and IV are unjustified universals.

Final Answer:Only II and III follow.