Consider the following collection of relations and dependencies. Assume that eac

Question

Consider the following collection of relations and dependencies. Assume that each relation is obtained through decomposition from a relation with attributes ABCDEFGHI and that all the known dependencies over relation ABCDEFGHI are listed for each question. State whether the relation is in BCNF. If it is not in BCNF, decompose it into a collection of BCNF relations

R1(A,B,C,D,E), A -> B, C -> D

The answer is that it is not in BCNF and the BCNF decomposition is AB, CD, ACE. Could someone please explain how they got the BCNF decomposition?

Explanation / Answer

Using the following simple algorithm not down it ,it is very help full for you

Initialize S = {R}

While S has a relation R' that is not in BCNF do:  

   Pick a FD: X->Y that holds in R' and violates BCNF

   Add the relation XY to S

   Update R' = R'-Y

Return S

Sol: Given R1(A,B,C,D,E), A -> B, C -> D

Step1:

Intialization S = {R}

S = {ABCDE}

Step2:

Pick FD: A->B which violates BCNF

S = {ACDE, AB}

Step3:

Pick FD: C->D which violates BCNF

S = {ACE, AB, CD}

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