Determine which of the provided conclusions logically follow from the given statement, assuming the statement to be true, and select the correct option.

Statement:
&@ > *% = #% < @$, #% > @! ≤ *^

Conclusions:
I. *% > @!
II. *^ < &@

Correct Answer: Conclusion I alone is correct

Let us analyze the given statement step-by-step to test the validity of each conclusion.

Given Statement:

&@ > *% = #% < @$, #% > @! ≤ *^

We can combine the relevant parts of the inequality chains for each conclusion.

Evaluating Conclusion I: *% > @!

From the statement, we have:

*% = #%

and

#% > @!

Substituting *% for #%, we get:

*% > @!

Therefore, Conclusion I is logically true.

Evaluating Conclusion II: *^ < &@

From the statement, we look at the path connecting &@ and *^:

&@ > *% = #% > @! ≤ *^

Here, we have a greater than sign (>) followed by a less than or equal to sign (≤) between #% (or &@) and *^. Due to the presence of opposite inequality signs (> and ≤) in the relationship chain between &@ and *^, no definitive relationship can be established between &@ and *^.

Therefore, Conclusion II does not logically follow.

Thus, only Conclusion I is correct.