Consider the statement to be true and decide which conclusions follow. Statement: No man is a donkey. Ajay is a man. Conclusions: I. Ajay is not a donkey. II. All men are not Ajay.

Introduction / Context:
This is a simple syllogism-style question involving a categorical statement and a specific instance. You are told that no man is a donkey and that Ajay is a man. From this, you must judge which of the two conclusions logically follow. The question also checks whether you misinterpret the second conclusion, which is phrased in an odd way.

Given Data / Assumptions:

Statement 1: No man is a donkey (i.e., the sets “men” and “donkeys” are disjoint).
Statement 2: Ajay is a man.
Conclusion I: Ajay is not a donkey.
Conclusion II: All men are not Ajay (interpreted as “no man other than Ajay exists” or “every man is different from Ajay”).

Concept / Approach:
For Conclusion I, we simply apply the general statement to the specific case: if no man is a donkey, then any particular man cannot be a donkey. For Conclusion II, we examine whether anything in the statements tells us how many men exist or whether Ajay is unique among them. Logical conclusions must be strictly based on the given information and not on additional assumptions.

Step-by-Step Solution:
From “No man is a donkey”, we know that the set of men and the set of donkeys have no overlap. From “Ajay is a man”, we know Ajay belongs to the set of men. Therefore, Ajay cannot also belong to the set of donkeys. So Conclusion I, “Ajay is not a donkey”, is a direct and valid consequence of the statements. Now consider Conclusion II: “All men are not Ajay.” This wording is ambiguous, but in standard reasoning it usually suggests some claim about the uniqueness or non-uniqueness of Ajay among men. The original statements say nothing about how many men there are or whether anyone else besides Ajay exists. Thus we cannot conclude anything about whether all men are distinct from Ajay or whether Ajay is the only man. The statement simply does not provide this information. Therefore, Conclusion II does not logically follow from the given statements.

Verification / Alternative check:
You can construct two possible worlds consistent with the statements: one where Ajay is the only man in the world, and another where there are many men besides Ajay. Both satisfy “No man is a donkey” and “Ajay is a man,” but they treat Conclusion II differently. Because the truth of Conclusion II changes between valid scenarios, it cannot be considered a necessary conclusion.

Why Other Options Are Wrong:
Options stating that both conclusions follow are incorrect because Conclusion II is not forced. Saying that neither follows ignores the direct link between the universal statement and the specific instance in Conclusion I. Any option that tries to impose extra conditions about the number of men is going beyond the given data.

Common Pitfalls:
A common error is to be thrown off by the awkward phrasing in Conclusion II and either accept or reject it without analysis. Carefully separating what is actually stated from what is not is vital. Another pitfall is forgetting that “no A is B” immediately tells you that a specific A cannot be B, which is the essence of Conclusion I.

Final Answer:
Only Conclusion I necessarily follows from the given statements. The correct option is Only conclusion I follows.