3. You're running an n week course and trying to plan all of your lectures ahead of time (I guess that's one way to do it). You have a set of m potential lecture topics T, where each topic will take one week to cover. Furthermore, due to constraints of the material not all lecture topics can be taught in any given week. Instead, in week i one topic of the set Ti can be chosen, where Ti CT. The diffieult part is you have k students each of which are doing different projects for the course. Each of these k projects has a set of related lecture topic: project j has a set of topics Pj S T. To be fair to the students, each project must have at least one of the related topics covered in the overall schedule. Let the problem of determining the schedule be called the Project Planning Problem (PPP) Assume that a solution for PPP takes in all necessary information regarding the problem and returns "yes" is schedule exists, and returns "no" if it doesn't. Show that 3-SAT Sp PPP. [12] 3. You're running an n week course and trying to plan all of your lectures ahead of time (I guess that's one way to do it). You have a set of m potential lecture topics T, where each topic will take one week to cover. Furthermore, due to constraints of the material not all lecture topics can be taught in any given week. Instead, in week i one topic of the set Ti can be chosen, where Ti CT. The diffieult part is you have k students each of which are doing different projects for the course. Each of these k projects has a set of related lecture topic: project j has a set of topics Pj S T. To be fair to the students, each project must have at least one of the related topics covered in the overall schedule. Let the problem of determining the schedule be called the Project Planning Problem (PPP) Assume that a solution for PPP takes in all necessary information regarding the problem and returns "yes" is schedule exists, and returns "no" if it doesn't. Show that 3-SAT Sp PPP. [12]