Statements : Some desks are caps. No cap is red. Conclusions : I. Some caps are desks. II. No desk is red.

The correct answer is: Only conclusion I follows.

The first statement is “Some desks are caps.” This means that there exists at least one desk that is also a cap. The second statement is “No cap is red.” This means that no object that is a cap is also red.

From these two statements, we can conclude that there exists at least one desk that is not red. However, we cannot conclude that all desks are not red. For example, it is possible that there exists a desk that is both a cap and red.

Therefore, only conclusion I follows. Conclusion II does not follow.

Here is a more detailed explanation of each option:

• Option A: Only conclusion I follows. This is the correct answer.
• Option B: Only conclusion II follows. This is incorrect. We cannot conclude that all desks are not red.
• Option C: Either I or II follows. This is incorrect. Only conclusion I follows.
• Option D: Neither I nor II follows. This is incorrect. Conclusion I follows.
• Option E: Both I and II follow. This is incorrect. Only conclusion I follows.