Syllogism — Determine which conclusion(s) necessarily follow: Statements: • Some buses are four-wheelers. • All four-wheelers are vans. Conclusions: I. Some vans are buses. II. Some buses are vans.

Introduction / Context:
This problem combines one particular and one universal statement. We must decide whether one or both of two seemingly similar conclusions are logically compelled.

Given Data / Assumptions:

• Some Buses are Four-wheelers (Buses ∩ Four ≠ ∅).
• All Four-wheelers are Vans (Four ⊆ Vans).

Concept / Approach:
The specific “some” elements that are Buses and Four-wheelers are, by the universal inclusion, also Vans. That one set of individuals witnesses both conclusions: they are Vans that are Buses (I) and Buses that are Vans (II).

Step-by-Step Solution:
1) Let x be an element with Bus(x) ∧ Four(x); such an x exists by premise.2) From Four(x) and Four ⊆ Vans, deduce Van(x).3) Therefore Bus(x) ∧ Van(x) holds for some x, proving both I (“Some vans are buses”) and II (“Some buses are vans”).

Verification / Alternative check:
A simple diagram with a Four subset within Vans and a Bus set overlapping Four at a non-empty region suffices; the overlap region lies inside Vans as well.

Why Other Options Are Wrong:
Any answer that keeps only one of I or II ignores the symmetry created by the same witness element.

Common Pitfalls:
Thinking I and II are different in force; they are contrapositive perspectives on the same intersection.

Final Answer:
Both conclusions I and II follow.