$(20$ points$)$

$($a$)$ Determine whether the following argument is valid:

She is a Math Major or a Computer Science Major.

If she does not know discrete math, she is not a Math Major.

If she knows discrete math, she is smart.

She is not a Computer Science Major.

Therefore, she is smart.

$($b$)$ Determine whether the following argument is valid.

If you are not in the tennis tournament, you will not meet Ed$.$

If you aren't in the tennis tournament or if you aren't in the play, you won't meet Kelly. You meet Kelly or you don't meet Ed$.$

It is false that you are in the tennis tournament and in the play.

Therefore, you are in the tennis tournament.

Solution: