Consider a set of functional dependencies F = {AB C, C AD, A B} on a relation schema R(A, B, C, D). (a) (10 points) Show the steps of computing a canonical cover for F. (b) (10 points) Determine whether or not AD is a candidate key using the transitive closure of some attributes. (c) (10 points) Assume that R is decomposed into R1(A, B) and R2(A, C, D). Is this decomposition dependency preserving? Justify your answer. (d) (10 points) Determine whether or not R(A, B, C, D) is in BCNF and justify your answer using the transitive closure of a set of attributes. If R(A, B, C, D) is not in BCNF, find a BCNF decomposition of it. (e) (10 points) Assume that R(A, B, C, D) is decomposed into R1(A, B) and R2(B, C, D). Given the above functional dependencies, is this decomposition lossy? Justify your answer.