Consider the following relation R with set of functional dependencies F R(DEFHIJ

Question

Consider the following relation R with set of functional dependencies F

R(DEFHIJ)

F={ DHJ-->EFI, FI-->HJ, DI-->EF, I-->E}

a. list all the candidate keys for this relation

b.what is the highest normal form R is in, considering up to and including BCNF? Justify your answer, that is, explain why R is not in a higher normal form than what you claim.

c. decompose the relation into a lossless join, FD-preserving decomposition. All resulting subrelations must be in BCNF.

d. Prove that your decomposition is a lossless join decomposition.

Explanation / Answer

(a) DI

(b) 1NF. Since the Functional Dependency I-->E is an partial dependency if DI is the primary key.So 2NF doesn'tcontain partial dependencies.

(c) The subrelations are R1 = {DHJ-->FI}, R2 = {FI-->HJ}, R3 = {DI-->F} and R4 = {I-->E}. All are in BCNF.

(d) Here R1?R2?R3?R4 = R. So as per the rule, as natural join of four sub relations is the original relation.It is a losless join decomposition

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