Show that the relation schemas produced by Algorithm 15.5 are in BCNF.

Algorithm 15.5. Relational Decomposition into BCNF with Nonadditive Join Property

Input: A universal relation R and a set of functional dependencies F on the attributes of R.

1. Set D := {R} ;
2. While there is a relation schema Q in D that is not in BCNF do

{
choose a relation schema Q in D that is not in BCNF;

find a functional dependency X → Y in Q that violates BCNF;

replace Q in D by two relation schemas (Q − Y) and (X ∪ Y);

} ;