Syllogism with negatives: 'All poles are guns' and 'Some boats are not poles' — determine which conclusions necessarily follow (All guns are boats; Some boats are not guns)

Given data

• Premise 1: Poles ⊆ Guns.
• Premise 2: Some Boats ⊄ Poles (i.e., ∃ Boats that are not Poles).
• Conclusions:
  • I: All Guns ⊆ Boats.
  • II: Some Boats ⊄ Guns.

Concept/Approach (why this method)

From 'Poles ⊆ Guns' we cannot reverse to 'Guns ⊆ Poles' or to 'Guns ⊆ Boats'. Also, 'Some boats are not poles' tells nothing about whether those boats are guns.

Step-by-Step calculation / logic
1) Conclusion I requires every gun to be a boat; no premise supports this ⇒ not necessary.2) For Conclusion II, the boats that are not poles could still be guns (if some guns are not poles) or might not be guns; both models satisfy premises ⇒ not necessary.

Verification/Alternative

Construct Model A where every gun is also a boat (I true) and Model B where many guns are not boats (I false); both fit premises. Hence I does not necessarily follow. Similar variability shows II does not necessarily follow.

Common pitfalls

• Illicit conversion of subset relations.
• Assuming 'not pole' implies 'not gun' (it does not).

Final Answer
Neither I nor II follows.