Category logic with subset and particular statement: from 'All birds are tall' and 'Some tall are hens', decide which conclusions are compelled (Some birds are hens; Some hens are tall)

Given data

• Premise 1: Birds ⊆ Tall.
• Premise 2: Some Tall are Hens (∃ Tall ∩ Hens).
• Conclusions:
  • I: Some Birds are Hens.
  • II: Some Hens are Tall.

Concept/Approach (why this method)

Only overlap explicitly stated is Tall ∩ Hens. Birds are inside Tall, but we do not know whether they overlap the particular Tall elements that are Hens.

Step-by-Step calculation / logic
1) From Premise 2, there exists at least one Hen that is Tall ⇒ II is necessarily true.2) Premises do not force any intersection between Birds and Hens ⇒ I is not necessary.

Verification/Alternative

Construct Tall containing disjoint subsets: Birds and Hens non-overlapping; both premises hold and I fails, proving I is not necessary while II remains true.

Common pitfalls

• Assuming all subsets of Tall intersect.

Final Answer
Only conclusion II follows.