Consider the schema R =(ABCDEFGH , {BE ? GH , G ? FA , D ? C , F ? B}).
a. Can there be a key that does not contain D? Explain.
b. Is the schema in BCNF? Explain.
c. Use one cycle of the BCNF algorithm to decompose R into two subrelations. Are the subrelations in BCNF?
d. Showthat your decomposition is lossless.
e. Is your decomposition dependency preserving? Explain.
a. No - Since D is not uniquely determined by any other attributes, it must be part of all keys.
b. No - None of the left hand sides are superkeys.
c. We can choose any of the FD as a basis for a decomposition. For example, R1 = (ABDEFGH , {BE ? GH , G ? FA , F ? B}), R2 =(DC , {D ? C}). In this case R1 is not in BCNF (since the LHS of all its FDs are not superkeys), but R2 is.
d. {ABDEFGH }?{CD} is a key of R2.
e. The decomposition is dependency preserving because each of the FDs of R is a FD of one of the component relations.
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