Consider the relation Courses(C,T,H,R,S,G), whose attributes may bew thought of informally as course, teacher, hour, room, student, and grade. Let the set of FD's for Courses be C → T, HR → C, HT → R, HS → R, and CS → G. Intuitively, the first says that a course has a unique teacher, and the second says that only one course can meet in a given room at a given hour. The third says that a teacher can be only one room at a given hour, and the fourth says the same about students. The last says that students get only one grade in a course. 1) What are all the keys for Courses? 2) Indicate all the 3NF violations. 3) Use the 3NF synthesis algorithm to find a lossless-join, dependency-preserving decompostion of R into 3NF relation.