In order for an argument to be sound, it must first be valid. So we must find out if this argument is valid.
An argument is valid if and only if the conclusion must be true if the premises are true. Here, we have two premises:
- All students are brilliant.
- She is brilliant.
We have one conclusion:
- She is a student.
So we ask: can she be something other than a student and still be brilliant?
The answer is yes -- nothing in the two premises says that only students can be brilliant. All students are brilliant, but that does not mean that other people cannot be brilliant.
Therefore, this argument is not valid. If an argument is not valid, it cannot be sound either.