Prove that each of the following argument is valid by defining each proposition with a

variable to obtain the form of the argument. Then use the rules of inference to prove

that the argument is valid.

(a) If I drive on the freeway, I will see the fire.

I will drive on the freeway or take surface streets (or both).

I am not going to take surface streets.

I will see the fire.

(b) If it was not foggy or it didnt rain (or both), then the race was held and there

was a trophy ceremony.

The trophy ceremony was not held.

It rained.