Please I need answer to these questions (11,12,13,14 and 15) thank you

11. Use a truth table to prove the conclusion from the hypotheses. The hypotheses are: (10 pts) a. If I drive on the freeway, I will see the fire. b. I will either drive on the freeway or take surface streets c. I am not going to take surface streets. Conclude that I will see the fire. Use the following variable names: . p: I drive on the freeway r: I take surface streets .q: I see the fire 12. Use the laws of logic to prove the conclusion from the hypotheses. Give propositions and predicate variable names in your proof. Use the set of all students as the domain of discourse. (10 pts) The hypotheses are a. Larry and Hubert are taking Boolean Logic. b. Any student who takes Boolean Logic can take Algorithms 8:42 1 The hypotheses are: a. Larry and Hubert are taking Boolean Logic. b. Any student who takes Boolean Logic can take Conclude that Larry and Hubert can take 13. Use the laws of logic to prove the conclusion from the hypotheses. Give propositions and predicate variable names in your proof. Use the set of all people as the domain of discourse. (10 pts) The hypotheses are: a. Everyone who practices hard is a good b. There is a member of the orchestra who practices hard. Conclude that someone in the orchestra is a good 14. Which of the following arguments are valid? Explain your reasoning. (8 pts) a. I have a student in my class who is getting an A Therefore, John, a student in my class is getting an A b. Every girl scout 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. 15. Use the laws of logic to show that x(Px) A Q(x)) implies that Vx Q(x) A Vx P(x). (6 pts)