Statements: All lasers are rays. All sun are rays. Conclusions: I. Some sun…

Concept:

When two premises are both universal affirmative statements that share only a common predicate term (All A are B, and All C are B), the middle term (B) is not distributed in either premise, so no relationship between the two subject terms (A and C) can be validly drawn on its own. The one exception: if two proposed conclusions about A and C form an exact complementary pair — a particular affirmative (“Some C are A”) and its exact contradictory universal negative (“No C is A”) — and neither follows individually, then because these are the only two exhaustive possibilities for how A and C relate, exactly one of them must be true.

Application:

Statements: All lasers are rays; All sun are rays. Both share only the common predicate “rays” and say nothing about how “lasers” and “sun” relate to each other. Conclusion I (“Some sun are lasers”) and Conclusion II (“No sun is laser”) form exactly this complementary pair about the same two terms (sun, lasers), with no middle ground between them. Since neither follows individually from the statements, but together the pair covers every possible relationship between the two groups, exactly one of the two must be true.

Cross-check:

Picture “rays” as one large circle with “lasers” and “sun” each drawn as separate circles fully inside it. The statements fix only that both smaller circles sit inside the big one; they leave the two smaller circles free to overlap partially, fully, or not at all. So no single fixed conclusion about their overlap can be asserted with certainty — but since “some overlap” and “no overlap” are the only two exhaustive possibilities, one of them must hold, confirming the either–or result.

Result:

Either I or II is correct.