Syllogism — Hills, rivers, deserts, roads (tracking a “some” through a chain): Statements: • Some hills are rivers. • Some rivers are deserts. • All deserts are roads. Conclusions: I. Some roads are rivers. II. Some roads are hills. III. Some deserts are hills.

Introduction / Context:This problem requires you to trace an existential statement through a universal link. Be careful not to assume overlapping “some” groups unless the premises force it.

Given Data / Assumptions:

• ∃ (Hill ∩ River).
• ∃ (River ∩ Desert).
• Desert ⊆ Road.

Concept / Approach:From “Some rivers are deserts” and “All deserts are roads,” at least one entity is both River and Road. That validates I. However, there is no requirement that the Hill∩River elements are the same rivers that are deserts; thus II and III are not compelled.

Step-by-Step:1) Take an element from River ∩ Desert (guaranteed).2) Map via Desert ⊆ Road to get River ∩ Road → Conclusion I.3) II “Some roads are hills” would need the desert-river elements to also be hills; not forced.4) III “Some deserts are hills” also requires the “some” groups to coincide; not forced.

Common Pitfalls:Transferring “some” across unrelated intersections or assuming identity of different existential subsets.

Final Answer:Only conclusion I follows.