Problem 5. A research lab is working on multiple projects where on every project there are multiple students involved. It is also possible that some students are involved in multiple projects. The lab wants to hold review meetings for as many projects as possible on a particular day. These meetings happen simultaneously, so that every student can attend at most one meeting. There is also a constraint that a meeting of any project can happen only if all the students involved in that project can attend the meeting. We are interested in finding the maximum number of meetings that the lab can organize on the particular day under these constraints. Formulate this problem as a graph theory