Problem 3. Teaching (8 points) The year is 2008 and you are reviewing the course schedule for next semester. There are 107 computer science students and each class is taken by exactly 25 students. Students are divided by the popular (yet likely terrible - never saw it myself) Twilight film, with 58 students being on "Team Jacob" (a werewolf), 42 students being on "Team Edward" (a vampire), and the remaining 7 students not caring one way or the other. Note that each student is on exactly one team, so we can partition the students into the subsets Edward (E), Jacob (J), and netiher (N). (a) [4 pts.] How many classes do you need to teach to ensure that at least one student is taking two of your classes? Briefly justify your answer. (b) [4 pts.] You are tasked with meeting with each of the students individually, but you don't yet know the order of the meetings. Regardless of the order, after how many meetings can you ensure that you will have met with an entire subset (whether that be E, J, or N)? Briefly justify your