Syllogism — Men, women, and intelligence: Statements: • No man is intelligent. • All women are intelligent. Conclusions to test: I. No man is a woman. II. No woman is a man.

Introduction / Context:
This problem checks whether learners can combine a universal negative with a universal affirmative to infer disjointness between two classes.

Given Data / Assumptions:

• No man is intelligent.
• All women are intelligent.

Concept / Approach:
If all women are intelligent, and no man is intelligent, then a person cannot simultaneously be a man and a woman; otherwise that person would be both intelligent (from being a woman) and not intelligent (from being a man), which is impossible. Hence the sets Man and Woman are disjoint.

Step-by-Step Solution:
1) From “All women are intelligent,” Woman ⊆ Intelligent.2) From “No man is intelligent,” Man ⊆ (not Intelligent).3) If any person were both Man and Woman, a contradiction would arise. Therefore, Man ∩ Woman = ∅.4) Conclusion I “No man is a woman” follows.5) Conclusion II “No woman is a man” is the same disjointness read in the other direction and also follows.

Verification / Alternative check:
Venn diagram: Woman inside Intelligent; Man entirely outside Intelligent; there is no overlap between Man and Woman.

Why Other Options Are Wrong:
Options stating only one or neither ignore that both directions of disjointness are equivalent.

Common Pitfalls:
Confusing “No man is intelligent” with “No intelligent person is a man” (illicit converse). The conclusion here is about gender sets, not the converse of premises.

Final Answer:
Both I & II follow.