Syllogism — Stones, gold, and banks (don’t force extra overlap): Statements: (a) Some stones are gold. (b) Some gold are banks. Conclusions to test: I. Some banks are stones. II. Some gold are stones. III. No stone is bank. IV. Some banks are gold.

Introduction / Context:
The premises provide two separate “some” relationships that share the class “gold.” The trap is to assume those “some” subsets are the same individuals, which is not required.

Given Data / Assumptions:

• ∃ (Stone ∩ Gold).
• ∃ (Gold ∩ Bank).

Concept / Approach:
Statements with “some” guarantee existence of at least one element in the intersection but do not identify which elements. Therefore, the overlap between Stone and Bank is undetermined, while the two direct conclusions about the given overlaps must hold.

Step-by-Step Assessment:
1) II “Some gold are stones” is exactly premise (a) restated and hence follows.2) IV “Some banks are gold” is exactly premise (b) restated and hence follows.3) I requires the two “some” groups to coincide; that is not necessary.4) III contradicts premise (b) if banks exist; in any case, it is not compelled by the premises.

Common Pitfalls:
Forcing a transitive “some” across two intersections or assuming disjointness without evidence.

Final Answer:
Only conclusions II and IV follow.