Syllogism — Evaluate the conclusions from the following statements: Statements: • All pins are rods. • Some rods are chains. • All chains are hammers. Conclusions: I. Some pins are hammers. II. Some hammers are rods. III. No pin is a hammer. Choose the option that correctly identifies which conclusion(s) follow logically.

Introduction / Context:
This question tests classical categorical syllogism. We must determine which conclusions necessarily follow from the given premises, not what could be true. The terms are “pins,” “rods,” “chains,” and “hammers.”

Given Data / Assumptions:

• All pins are rods.
• Some rods are chains.
• All chains are hammers.

Concept / Approach:
Translate the statements into set relations. “All X are Y” means X ⊆ Y. “Some X are Y” indicates a non-empty intersection. Only conclusions that are true in every model consistent with the premises can be marked as “follows.”

Step-by-Step Solution:
1) From “Some rods are chains” and “All chains are hammers,” we get: some rods are hammers.2) From “All pins are rods,” pins are a subset of rods, but there is no claim that any pins are among those rods that are chains.3) Therefore, it is possible that no pin belongs to chains (and thus to hammers). Hence “Some pins are hammers” is not necessary.4) Likewise, “No pin is a hammer” is not necessary either because pins could overlap with the chain portion of rods in some models.5) However, “Some hammers are rods” is guaranteed because those rods that are chains are also hammers.

Verification / Alternative check:
Construct two models: (a) pins entirely outside chains (I false, II true, III true); (b) pins overlapping chains (I true, II true, III false). Only conclusion II remains true across all models.

Why Other Options Are Wrong:

• I (“Some pins are hammers”): possible but not necessary.
• III (“No pin is a hammer”): possible but not necessary.
• “Either I or III” with II: the “either-or” part is not guaranteed; only II is certain.

Common Pitfalls:
Confusing “can be” with “must be,” and assuming subsets necessarily intersect without explicit information.

Final Answer:
Only II follows.