EXERCISE 1.12.4: Proving arguments in English are valid using rules of inference. Prove that each argument is valid by replacing each proposition with a variable to obtain the form of the argument. Then use the rules of inference to prove that the form 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 didn't rain (or both), then the race was held and there was a trophy ceremony. The trophy ceremony was not held. It rained. (c) If I work out hard, then I am sore. If I am sore, I take an aspirin. I did not take an aspirin. I did not work out hard