(10 pts) Let n > 3 be a natural number. Consider Kn, an airline with n airports across the nation. For every (unordered) pair of airports, there is one airplane that flies between them (both ways). To cut costs, the airline wants to get rid of some of these airplanes. (a) Let k be the minimum number of airplanes that must be removed such that the resulting network has no cycles, but it is still possible to go from any airport to any other airport through a series of flights. Determine the value of k as an expression in terms of n. Then indicate how to remove the minimum number of airplanes from Kn to achieve this goal. (b) As an alternate way to cut costs, the airline considers getting rid of some of the airports. Let l be the minimum number of airports that must be removed (removing a location removes the airplanes that travel to it) such that the new network has no cycles but it is still possible to travel from any airport to any other airport through a series of flights. Determine the value of l as an expression in terms of n. Then indicate how to remove the minimum number of airports of Kn to achieve this goal.