Statements: • Some cars are buses. • All cars are caves. Conclusions: I. Some caves are not buses. II. Some caves are buses. III. No cave is a bus. IV. Some caves are cars. Select the option that must follow.

Introduction / Context:
This question pairs one existential overlap with a universal inclusion. We must track how elements propagate through inclusions to evaluate what necessarily holds about the larger set “caves.”

Given Data / Assumptions:

• Premise 1: Some Cars are Buses (∃x ∈ Cars ∩ Buses).
• Premise 2: All Cars are Caves (Cars ⊆ Caves).

Concept / Approach:
If all Cars are Caves, then every car— including those that are buses— is also a cave. Therefore, the intersection established in Premise 1 immediately gives an intersection within Caves. Separately, “Some caves are cars” follows because all cars are caves and there exists at least one car (witnessed by Premise 1).

Step-by-Step Solution:
1) From “Some Cars are Buses,” pick witness c1 ∈ Cars ∩ Buses.2) From “All Cars are Caves,” c1 ∈ Caves. Therefore, c1 ∈ Caves ∩ Buses ⇒ Conclusion II is true (Some Caves are Buses).3) Because at least one Car exists, and all Cars are Caves, it follows that Some Caves are Cars ⇒ Conclusion IV is true.4) Conclusion I (“Some Caves are not Buses”) is not forced; it could be that every cave is a bus, or not— the premises do not settle this.5) Conclusion III (“No Cave is a Bus”) directly contradicts II and cannot be true in all models.

Verification / Alternative check:
Model: Let Cars = {c1}, Buses = {c1}, Caves = {c1, c2}. All Cars are Caves; Some Cars are Buses. Then II and IV hold; I might or might not hold depending on whether c2 is a bus— hence I is not necessary. III is false.

Why Other Options Are Wrong:
Any option that includes I or III claims something not guaranteed by the premises or contradicts them.

Common Pitfalls:
Confusing “All Cars are Caves” with “Only Cars are Caves,” and assuming extra information about Buses outside what is asserted.

Final Answer:
Only Conclusions II and IV follow.