Syllogism — Test disjointness and existence carefully Statements: • All furniture are jungles. • No jungle is road. • Some roads are hills. Conclusions: I) Some roads are furniture. II) Some jungles are furniture. III) Some hills are jungles. Select what necessarily follows from the premises.

Introduction / Context:
This question checks whether you can keep track of disjoint sets and avoid drawing existential conclusions that are not warranted. We have a universal inclusion (furniture ⊆ jungles), a universal exclusion (jungles ∩ roads = ∅), and one existential fact (some roads are hills). The task is to see which of the proposed conclusions must hold in every model consistent with the premises.

Given Data / Assumptions:

• All furniture are jungles (Furniture ⊆ Jungles).
• No jungle is a road (Jungles ∩ Roads = ∅).
• Some roads are hills (∃x: x ∈ Roads ∩ Hills).

Concept / Approach:
When you have “No A is B,” any subset of A is also disjoint from B. Thus Furniture, being inside Jungles, is automatically disjoint from Roads. Also, “All A are B” does not by itself assert that A exists, so you cannot infer “Some B are A” unless there is a separate existence guarantee. Finally, an existential fact about Roads and Hills says nothing about Jungles unless a link is stated.

Step-by-Step Solution:

Verification / Alternative check:
Create a model where there is at least one road that is a hill, zero furniture items, and many jungles but none are roads. All premises are satisfied and none of the conclusions I–III holds.

Why Other Options Are Wrong:
Any option claiming I, II, or III follows ignores either the disjointness (for I) or the lack of existential guarantee (for II) or the absence of any bridge (for III).

Common Pitfalls:
Assuming existence from a universal (“All A are B” ⇒ “Some B are A”) and casually linking unrelated sets.

Final Answer:
None of these.