Consider the following statements followed by two conclusions:

Statements : Some men are great.
                         Some men are wise.

Conclusion I : Men are either great or wise.
Conclusion II : Some men are neither great nor wise.

Which one of the following is correct?

The correct option is Neither of the conclusions is valid.

Let us analyze the statements and conclusions step-by-step using logical reasoning and Venn diagrams.

Analyzing the Statements:
1. "Some men are great": This means there is an intersection between the set of men and the set of great people. It does not mean all men are great, nor does it define the status of the remaining men.
2. "Some men are wise": This means there is an intersection between the set of men and the set of wise people. Similarly, it does not apply to all men.

Evaluating Conclusion I (Men are either great or wise):
This conclusion asserts that every single man must fall into at least one of the two categories: great or wise. However, the statements only tell us about some men. There could exist men who are neither great nor wise. Since we cannot guarantee that every man is either great or wise based on the premises, Conclusion I is not logically valid.

Evaluating Conclusion II (Some men are neither great nor wise):
While it is possible that there are men who are neither great nor wise, the statements do not explicitly force this condition. For example, if the set of "men" is entirely composed of some who are great and others who are wise (or some who are both), there might not be any man left who is neither. Because we cannot say with absolute certainty that there must be some men who are neither great nor wise, Conclusion II is also not logically valid.

Therefore, neither conclusion follows necessarily from the given statements.