Is the following argument sound? All students are brilliant. She is brilliant. So she is a student.

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.