Prove if the following is valid or not by using proof by falsification: a. If 4 megabytes of memory is better than no memory at all, then either we will buy new computer or we w ill buy more memory. If we will buy a new computer, then we will not buy more memory. Therefore, if 4megabytes of memory is better than no memory at all, then we will buy a new computer. b. Today is Tuesday or Wednesday. But it can't be Wednesday, since the doctor's office is open today, and that office is always closed on Wednesdays. Therefore, today must be Tuesday. Represent the following in proposition logic: a. It snows whenever the wind blows from the northeast. b. It is necessary to read the textbook to understand the materials of this course. c. For a number to be divisible by 3, it is sufficient that it is the sum of three consecutive integers. d. Your guarantee is good only if you bought your TV less than 90 days ago. e. If you send me an e-mail message, then I will finish writing the program. If you do not send me an e-mail message, then I will go to sleep early. If I go to sleep early, I will wake up feeling refreshed. Therefore, if I do not finish writing the program, then I will wake up feeling refreshed