Recall that in the activity selection problem, we are given the start and finish times of n activities and the goal is to find the maximum size subset of compatible activities. Note that activities ai and aj are compatible if the intervals [si , fi) and [sj , fj ) do not overlap. Consider each of the following greedy selection heuristics. Each one is repeated until no activities to select remains. For each one prove or disprove whether it finds the optimum.

(a) Among the remaining activities that are compatible with previously selected activities, select the last activity to start.

(b) Among the remaining activities that are compatible with previously selected activities, select the activity of least duration.

(c) Among the remaining activities that are compatible with previously selected activities, select the activity that overlaps the fewest other remaining activities.