In this statement and conclusion question, you must consider the given statements as true and decide which conclusions can definitely be drawn. Statement 1: Some girls are stars. Statement 2: Meena is a girl. Conclusion I: Meena is a star. Conclusion II: Some stars are not girls.

Introduction / Context:
This question involves reasoning with partial information about the sets girls and stars, along with a specific individual named Meena. The aim is to see whether we can conclude that Meena belongs to the set of stars or that some stars are outside the set of girls. You must resist the temptation to over interpret the phrase "some girls are stars" and instead work with its exact logical meaning.

Given Data / Assumptions:
- Statement 1: Some girls are stars, which means the intersection of the sets girls and stars is non empty.
- Statement 2: Meena is a girl, which means Meena belongs to the set of girls.
- Conclusion I: Meena is a star, which asserts that Meena belongs to the star set.
- Conclusion II: Some stars are not girls, which asserts that there is at least one star outside the set of girls.

Concept / Approach:
Let G represent the set of girls and S represent the set of stars. The statement "some girls are stars" can be written as G ∩ S is non empty. This tells us that there exist at least some individuals who are both girls and stars, but it does not identify them. The fact that Meena is a girl places her in G but does not tell us whether she lies in the overlapping part with S or in the part of G outside S. Similarly, the statement does not specify whether S has members outside G.

Step-by-Step Solution:
Step 1: From Statement 1, there exist some individuals who are both girls and stars, but their identities are unknown. Step 2: From Statement 2, Meena is in G, the set of girls. Step 3: Meena could be one of the girls who are stars, or she could be one of the girls who are not stars. The information given does not specify which case applies. Step 4: Because we cannot be sure that Meena belongs to the subset of girls that are stars, Conclusion I, "Meena is a star," does not logically follow. Step 5: Now consider Conclusion II, "Some stars are not girls." For this to follow, S must have at least one element outside G. Step 6: However, Statement 1 only tells us that some portion of G overlaps S. It does not state whether S has any part outside G or lies completely inside G. Step 7: It is possible that all stars are girls, that no stars are girls except a few, or anything in between. Since the statements do not constrain S beyond having some overlap with G, we cannot conclude that some stars are not girls.

Verification / Alternative check:
Construct two example diagrams. In Diagram A, let all stars be girls, so S is entirely inside G. This satisfies the statement "some girls are stars" and makes Conclusion II false because no star is outside G. In Diagram B, let S overlap G partly but extend outside G as well. This satisfies the same statement but makes Conclusion II true. Because the same statements can lead to different truth values for Conclusion II, it does not follow logically. Similarly, Meena can be placed either in the overlapping region G ∩ S or in the part of G that is outside S without breaking any statement, so Conclusion I also does not follow.

Why Other Options Are Wrong:
Option A assumes Meena is one of the girls who are stars, which is not guaranteed. Option B assumes that S definitely extends beyond G, which we cannot infer. Option C claims both conclusions follow, which is even stronger and clearly false. Option E describes a possibility, but the question asks which conclusions must follow, not what may be possible. The only accurate choice is that neither of the given conclusions is logically forced.

Common Pitfalls:
A common mistake is to think that "some girls are stars" implies that every girl involved must be a star, especially when a specific name is mentioned. Another error is to assume that if two sets overlap, at least one of them must have elements outside the other. In fact, two sets can overlap with one completely contained in the other, or each having non overlapping parts. Logical questions require you to consider all consistent possibilities, not just the ones that feel most natural at first glance.

Final Answer:
The correct option is Neither conclusion I nor II follows, because we cannot be sure that Meena is among the girls who are stars, and we cannot be sure that there is any star outside the set of girls.