Consider the relation schema TEACH={Course, Professor, Time, Room, Student, Grade} with the following set of Functional Dependencies (FDs): Course Professor {Time, Room} Course {Time, Professor) Room {Time, Student} Room {Student, Course) Grade 1 What are the prime attributes of TEACH? Justify your answer (i.e., show the main steps and your working used for computing the prime attributes). 2 Justify whether TEACH is in BCNF with respect to . If TEACH is not in BCNF with respect to . identify a BCNF decomposition for TEACH (you need to show the main steps used for identifying this BCNF decomposition) and justify whether this BCNF decomposition is dependency preserving.