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)
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
Answer
Correct Answer: Only conclusion II follows
Explanation
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 / logic1) 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 AnswerOnly conclusion II follows.