Problem 2. Recall the job scheduling problem. The input is composed of the starting and finishing times of n jobs. We would like to find the maximum set of pairwise disjoint jobs. Consider the following alternative greedy algorithms for the job scheduling problem. For each algorithm, either prove or disprove (by presenting a counter example) that it always constructs an optimal schedule (a) Choose the job that ends last, discard all conflicting jobs, and recurse. (b) Choose the job that starts first,discard all conflicting jobs, and recurse. (c) Choose the job that starts last, discard all conflicting jobs, and recurse. (d) Choose the job with shortest duration, discard all conflicting jobs, and recurse