Consider the relation Courses (C, T, H, R, S, G), whose attributes may be 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 in 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.

a) Find the minimal basis for the given FDs using method shown in class.

b) Use the 3 NF synthesis algorithm to find a lossless- join, dependency -preserving decomposition of Courses into 3 NF relations.

c) Use the chase test for lossless join to show that we can recreate the original courses relation with the same tuples using natural join of relations from b)