Consider the following set F of functional dependencies on the relation schema R$($A$,$ B$,$ C$,$

D$,$ E$)$:

AB $->$ C

A $->$ B

B $->$ D

C $->$ A

D $->$ CE

E $->$ BGive a lossless BCNF decomposition of r based on the set of functional dependencies.

Does the decomposition preserve dependencies? Why or why not?