Consider the following relational schema: Department(deptld, dname, locatlon) Student(snum, sname, deptld, age) Faculty(fld, fname, deptld) Class(cname, deptid, meets at, room, faculty) Enrolled(snum, cname, score, grade Assume that: - All students and faculty members must malor/work In one department; - Faculty teach courses only In the department they belong to; - The names of the courses are unlque for each department; - Scores are numbers In to,100]; - Faculty In Table Class Is a subset of fld In Table Faculty Wrlte each of the following querles using Datalog. If you belleve any one of the following Is not expresslble In Datalog, Informally explain why It cannot be expressed. 7. (10 pts) FInd the faculty who have Instructed at least one course In the CS department but have never Instructed any course In the Mathematics department 8. (10 pts) FInd the names of courses each student gets the lowest score In, .e., If a student takes 2 courses A and B and scores 50 and 60, respectlvely, then A Is the name of the course In whlch that student (can be different for different students depending on thelr score) has scored the lowest. 9. (15 pts) What are the posslble outcomes If a Datalog rule Is unsafe? Please Illustrate two dlfferent scenarlos for thls case by designing unsafe rules for the relatlonal schema mentloned above, and explain the answers to these rules