In this statement and conclusion question, you are given two statements relating stars, satellites, and the property of twinkling. Accept the statements as true, even if they differ from real world facts, then read the conclusions and decide which of them logically follows. Statements: (I) All stars twinkle. (II) All satellites twinkle. Conclusions: (I) Some stars are satellites. (II) Some stars twinkle.

Introduction / Context:
This is a basic syllogism question involving stars, satellites, and the act of twinkling. The statements describe two different sets, both fully contained within a larger conceptual set of twinkling objects. Your task is to decide which of the given conclusions necessarily follows from these statements under strict logical interpretation.

Given Data / Assumptions:

• Statement (I): All stars twinkle.
• Statement (II): All satellites twinkle.
• Conclusion (I): Some stars are satellites.
• Conclusion (II): Some stars twinkle.
• We assume that stars exist, so “all stars twinkle” implies at least one twinkling star.

Concept / Approach:
Both statements are universal. “All stars twinkle” means that the set of stars is a subset of the set of twinkling objects. “All satellites twinkle” means that the set of satellites is another subset of the same set. The key question is whether these two subsets are forced to overlap and whether we can infer existence of stars that twinkle. Logical conclusions must hold in every Venn diagram that respects the statements, not just in diagrams we find intuitive.

Step-by-Step Solution:
Step 1: Draw a large circle representing all twinkling objects.Step 2: Place the stars set completely inside this circle, as all stars twinkle.Step 3: Place the satellites set also completely inside the twinkling circle, because all satellites twinkle.Step 4: Notice that the problem does not say anything about stars being satellites or satellites being stars. So the two subsets can be disjoint inside the twinkling set or they may overlap; both arrangements are allowed.Step 5: Evaluate conclusion (I): “Some stars are satellites.” This requires at least one object that is both a star and a satellite. However, we can construct a valid diagram where stars and satellites are two separate non-overlapping regions inside the twinkling set. In that case, no star is a satellite. Therefore conclusion (I) is not guaranteed.Step 6: Evaluate conclusion (II): “Some stars twinkle.” Since all stars twinkle and we assume there is at least one star, it follows directly that at least one star twinkles. Consequently, conclusion (II) must be true in every acceptable diagram.

Verification / Alternative check:
Symbolically, from statement (I), for any object x, if x is a star then x twinkles. If there exists at least one star, call it s, then s is a star and therefore s twinkles. This is exactly what conclusion (II) expresses. For conclusion (I), we would need an object that is both star and satellite, but the statements do not establish any such link. Because it is logically possible that there is no object that belongs to both groups, we cannot accept conclusion (I) as a necessary consequence.

Why Other Options Are Wrong:
Option A says only conclusion (I) follows, but we just saw that conclusion (I) is not forced. Option C claims that neither conclusion follows, which ignores the straightforward implication that some stars twinkle. Option D says that both conclusions follow, which again overstates what is supported by the statements by including conclusion (I). Only option B, which accepts conclusion (II) and rejects conclusion (I), is consistent with correct logical reasoning.

Common Pitfalls:
Many learners mistakenly assume that if two categories share a common property, such as twinkling, then they must have some elements in common. This is not true in logic: two distinct subsets can be completely disjoint yet share the same superset property. Another error is to overlook the implicit existence of stars, which supports the move from “all stars twinkle” to “some stars twinkle” in the exam context.

Final Answer:
Therefore, the correct conclusion is that only conclusion (II) follows from the given statements.