Statements: • Some kings are queens. • All queens are beautiful. Conclusions: I. All kings are beautiful. II. All queens are kings. Choose the option that must follow.

Introduction / Context:
This item mixes a particular affirmative with a universal inclusion to test overgeneralization. From “some kings are queens” and “all queens are beautiful,” we can indeed infer “some kings are beautiful,” but neither of the offered conclusions matches that weaker, correct statement.

Given Data / Assumptions:

• Some Kings are Queens (∃x ∈ Kings ∩ Queens).
• All Queens ⊆ Beautiful.

Concept / Approach:
Because all queens are beautiful, any king who is also a queen is beautiful. That yields “some kings are beautiful,” not “all kings are beautiful.” The second conclusion, “All queens are kings,” is a converse of the first premise and is not entailed.

Step-by-Step Solution:
1) Take witness k1 ∈ Kings ∩ Queens. From Queens ⊆ Beautiful, k1 ∈ Beautiful.2) Therefore, “some kings are beautiful” is true. But Conclusion I states “all kings are beautiful,” which is stronger and unjustified.3) Conclusion II (“All queens are kings”) is a universalization not supported by “some kings are queens.”

Verification / Alternative check:
Model: Kings = {k1, k2}, Queens = {k1}, Beautiful = all queens ∪ others. Premises hold. I is false if k2 is not beautiful; II is false if there exists a queen not among kings in another model. Thus neither conclusion is necessary.

Why Other Options Are Wrong:
“Either … or …” suggests exactly one is forced; but we can build models where both fail, so option C is incorrect. “Both” obviously overstates.

Common Pitfalls:
Upgrading “some” to “all,” and confusing a statement with its converse.

Final Answer:
Neither Conclusion I nor Conclusion II follows.