Consider a relation R = (ABCDEF) with the following functional dependencies:

B → AC, CD → E, A → D, and E → C.

a. Find a functional dependency that violates BCNF. Explain why it is a violation.

b. Give a BCNF decomposition of the schema R into sub-schemes R1 and R2 based on the functional dependency found in a)

c. Among the given functional dependencies B → AC, CD → E, A → D, and E → C, list those with all attributes entirely in R1 (or R2). Identify a functional dependency on R1(or R2) that remains a BCNF violation on R1 (or R2).

d. Based on the violation found in part c), further decompose the subschema R1 (or R2).