First, come up with a relation with some functional dependencies. At least one of the functional dependencies violates BCNF and at least one other of the functional dependencies makes it not dependency-preserving. Now, do lossless-join decomposition into BCNF although it may not be dependency-preserving.

Second, come up with a relation with some functional dependencies that make it dependency-preserving but not lossless-join.

Explain every step.