We mentioned in Section 3.3.4 that we would exercise our option to expand the right side of an FD that is a BCNF violation if possible. Consider a relation R whose schema is the set of attributes {.4, B, C, D] with FDs A ? B and A ? C. Either is a BCNF violation, because the only key for R is {A, D}. Suppose we begin by decomposing R according to A ? B. Do we ultimately get the same result as if we first expand the BCNF violation to A ? B C? Why or why not?