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Consider the relation Courses(C, T, H, R, S, G), whose attributes may be thought of information 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 that the same about students. The last says that students get only one grade in a course.
Let’s choose the key of Courses?