Consider the following relation R with set of functional dependencies F R(DEFHIJ
ID: 3544600 • Letter: C
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