Consider a relation R(A,B,C,D,E) with the following functional dependencies:
A → B
A → C
BC → A
D → E
Decompose the relation R into a collection of Boyce-­‐Codd Normal Form (BCNF) relations. For each step, show the relation that you are decomposing and the violation of BCNF that you are using during that decomposition step.
Indicate clearly your end result: the relations, their attributes, and their keys. Does your decomposition preserve functional dependencies?