Problem 10 (8 points): Use the laws of logic to prove the conclusion from the hypotheses. Give propositions and predicate variable names in your proof. The hypotheses are: If I drive on the freeway, I will see the fire. I will either drive on the freeway or take surface streets. I am not going to take surface streets. Conclude that I will see the fire.

Problem 11 (8 points): Which of the following arguments are valid? Explain your reasoning. I have a student in my class who is getting an A. Therefore, John, a student in my class is getting an A. Every girl scouts who sells at least 50 boxes of cookies will get a prize. Suzy, a girl scout, got a prize. Therefore Suzy sold 50 boxes of cookies.

Problem 12 (8 points): Use the laws of logic to show that x(P(x) Q(x)) implies that x Q(x) x P(x).