Problem 1 The table below lists some prerequisite information for some subjects in the MIT Computer Science program (in 2006). This defines an indirect prerequisite relation,, that is a strict partial order on these subjects. 18.01 6.042 18.01 18.03 8.01 8.02 6.042 6.046 18.01 18.02 6.046 6.840 6.001 6.034 18.03, 8.02 6.002 6.001, 6.002 6.004 6.033 6.857 6.001, 6.002 6.003 6.004 6.033 (a Explain why exactly six terms are required to finish all these subjects, if you can take as many subjects as you want per term. Using a greedy subject selection strategy, you should take as many subjects as possible each term. Exhibit your complete class schedule each term using a greedy strategy (b) In the second term of the greedy schedule, you took five subjects including 18.03. Identify a set of five subjects not including 18.03 such that it would be possible to take them in any one term (using some nongreedy schedule). Can you figure out how many such sets there are? (c) Exhibit a schedule for taking all the courses-but only one per term. (d) Suppose that you want to take all of the subjects, but can handle only two per term. Exactly how many terms are required to graduate? Explain why. (e) What if you could take three subjects per term