Syllogism — Premises: All hens are cocks. No cock is black. Conclusions: I) All cocks are hens. II) No hen is black.

Difficulty: Easy

Correct Answer: Only conclusion II is valid

Explanation:


Introduction / Context:
This mixes a universal inclusion with a universal exclusion. We test each conclusion cautiously for direction and scope.


Given Data / Assumptions:

  • Hens ⊆ Cocks.
  • Cocks ∩ Black = ∅.


Concept / Approach:
From Hens ⊆ Cocks and no Cock is Black, we infer Hens ∩ Black = ∅, i.e., no hen is black (II). The first conclusion reverses inclusion and is not supported.


Step-by-Step Solution:

Step 1: Substitute: any hen is a cock.Step 2: Since no cock is black, that hen cannot be black.Step 3: Hence II holds. I fails because 'All cocks are hens' is the converse and need not be true.


Verification / Alternative check:
Model where some cocks are not hens satisfies premises but falsifies I.


Why Other Options Are Wrong:
Any option including I treats converse as valid; it is not.


Common Pitfalls:
Confusing subset with set equality.


Final Answer:
Only conclusion II is valid.

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