Syllogism — Evaluate conclusions based on two universal statements: Statements: • All students are boys. • No boy is dull. Conclusions: I. There are no girls in the class. II. No student is dull.

Introduction / Context:
Two universal premises are given about “students,” “boys,” and “dull.” We must decide which of two conclusions is necessary.

Given Data / Assumptions:

• Students ⊆ Boys.
• Boys ∩ Dull = ∅.

Concept / Approach:
From Students ⊆ Boys and the fact that no Boy is Dull, it follows immediately that no Student is Dull. However, nothing in the premises talks about “girls in the class.” Even if all Students are Boys, there could still be (non-student) Girls in the class, or none at all; the premises are silent about that.

Step-by-Step Solution:
1) Students ⊆ Boys and Boys ∩ Dull = ∅ ⇒ Students ∩ Dull = ∅ (no student is dull). Thus II is necessary.2) I claims “There are no girls in the class.” The premises do not refer to the presence/absence of girls; the statement is not entailed.

Verification / Alternative check:
Construct a model with Students entirely within Boys, and optionally include some Girls (not students) in the class. Premises remain true while I may be false, proving I does not follow.

Why Other Options Are Wrong:
Any option including I attributes information that was never provided.

Common Pitfalls:
Confusing the domain “students” with “everyone in the class,” and reading extra facts about gender distribution that are not stated.

Final Answer:
Only conclusion II follows.