Statements: a) All metals are silver. b) All silver are diamond. c) Some diamonds are gold. d) Some gold are marbles. Conclusions: I. Some gold are metals. II. All metals are diamond. III. Some silver are marble. IV. Some gold are silver. Select the option that must follow.

Introduction / Context:
This item tests multi-premise chaining and existence handling in categorical syllogisms. Universal inclusions can be chained; existential statements (“some …”) guarantee at least one element but do not force intersections with unrelated sets unless specified.

Given Data / Assumptions:

• All Metals ⊆ Silver.
• All Silver ⊆ Diamond.
• Some Diamonds are Gold (∃x: x ∈ Diamond ∩ Gold).
• Some Gold are Marbles (∃y: y ∈ Gold ∩ Marbles).

Concept / Approach:
From universal chains A ⊆ B and B ⊆ C we infer A ⊆ C. “Some” statements assert existence but do not identify overlap with a given other subset unless a link is stated or deducible.

Step-by-Step Solution:
1) Chain universals: Metals ⊆ Silver ⊆ Diamond ⇒ Metals ⊆ Diamond. So Conclusion II is necessarily true.2) Conclusion I (“Some gold are metals”): We only know some Diamonds are Gold. Metals are Diamonds, but nothing ensures that the particular Diamonds that are Gold are also Metals. Not entailed.3) Conclusion III (“Some silver are marble”): We know some Gold are Marbles and some Diamonds are Gold. That gives some Diamonds are Marbles, but Silver ⊆ Diamond does not imply any Silver is Marble. Not entailed.4) Conclusion IV (“Some gold are silver”): From “some Diamonds are Gold” and Silver ⊆ Diamond, Gold could intersect Silver or lie outside Silver entirely; not guaranteed.

Verification / Alternative check:
Create a model where Diamonds = {d1, d2}, Silver = {s1} with s1 = d1, Metals = {m1} with m1 = s1, Gold = {d2}, Marbles = {g1} with g1 = d2. All premises hold; only Conclusion II is forced.

Why Other Options Are Wrong:
Conclusions I, III, IV require overlaps not guaranteed by the premises.

Common Pitfalls:
Confusing “subset of Diamonds” with “equals the specific Diamonds that are Gold.” Existence in one region of a superset never forces existence in a particular subset unless stated.

Final Answer:
Only conclusion II follows.