(a) (8 pts.) Use a direct proof to prove that if v and z are rational numbers and z 75 0 then v/z is a rational number. Hint: We saw a direct proof involving rational numbers in Week 1's lecture on Direct Proofs, as well as in subsequent lectures and Tutorial 1. You should rst try to understand that proof before attempting this one. Don't forget to apply the problem solving process by trying the claim out on examples rst to get a sense for the result. Grading Notes. While a detailed rubric cannot be provided in advance as it gives away solution details1 the following is a general idea of how points are distributed for this problem. If you can at least get part-way. we give partial credit where we can. (6) Correctness. If your proof is not correct. this is where you'll get docked. (5) Regardless of how you formulate your proof, somewhere you'll need certain facts without which the proof wouldn't work. E.g. if it weren't true that the sum of two integers is integer, would your proof fail? If so, then that is a fact I need to see stated somewhere. (1) The order of these facts must make sense, so that you're not inferring something before you have all the facts to infer it. E.g. you cannot use the fact that the sum of two integers is integer if you don't already know that you have two integers to begin with. (2) Communication. We need to see a mix of notation and intuition, preferably in the \"column" format with the notation on the left, and the reasons on the right. If you skip too many steps at once, or we cannot follow your proof, or if your solution is overly wordy or confusing, this is where you'll get docked