Making Logical Arguments $[18$ points$]$

Prove the following using the appropriate rules of inference. You may assume that

your universe is all students.

Every student will either fly home or drive home for Thanksgiving.

A student will drive home only if she lives in the midwest and owns a car.

Claire does not live in the midwest.

Therefore, there is a student who does not live in the midwest and flies

home for Thanksgiving.

$($a$)[4$ Pts$]$ Define the predicates F$($x$),$ D$($x$),$ O$($x$),$ and L$($x$).$