Consider the schema R $=($A$,$ B$,$ C$,$ D$,$ E$,$ G$)$ and the set F of functional depen$-$

dencies:

A $->$ BC

BD $->$ E

CD $->$ AB

a$.$ Find a nontrivial functional dependency containing no extraneous at$-$

tributes that is logically implied by the above three dependencies and ex$-$

plain how you found it$.$

b$.$ Use the BCNF decomposition algorithm to find a BCNF decomposition

of R$.$ Start with A $->$ BC$.$ Explain your steps.

c$.$ For your decomposition, state whether it is lossless and explain why.

d$.$ For your decomposition, state whether it is dependency preserving and

explain why.