4. (25 points) Assume that you are in charge of scheduling the final exams in the Georgia Southern University. This is not easy because some students are taking several courses and a student can take only one test during a particular time slot. We say two courses have a conflict if there is a student taking both courses. In other words, two courses having a conflict cannot be scheduled at the same time slot. Prove by induction that if no course has more than k conflicts, you can schedule the exams in k+1 time slots. Solution