6. Consider a scheduling problem, where there are five activities to be scheduled in four time slots. Suppose we represent the activities by the variables A, B, C, D, and E, where the domain of each variable is {1,2,3,4} and the constraints are A > D, D > E, C + A, C > E, C + D, B > A, B+C, and C + D +1. [Before you start this, try to find the legal schedule(s) using your own intutions.] (a) Show how backtracking solves this problem. To do this, you should draw the search tree generated to find all answers. Indicate clearly the valid schedule(s). Make sure you choose a reasonable variable ordering. (b) Show how arc consistency solves this problem. To do this you must draw the constraint graph; show which elements of a domain are deleted at each step, and which arc is responsible for removing the element; show explicitly the constraint graph after arc consistency has stopped; and show how splitting a domain can be used to sove this