plz someone decompose it in BCNF

Question

$R(ABCD)$

 Functional depedndency  :  { $AB \rightarrow CD , D\rightarrow A$ }

AB and DB  are  candidate key 

Comments

@Anu007  thanks sir are you sure  tables  are (ABD) and (AD)  not  (AD) and (BCD)  as in image plz check it 

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there are multiple tables possible but one thing for sure all dependency is not preserved like here in you image

AB-> C is not preserved.

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thanks sir

Answer 1

for the table R(A,B,C,D), the candidate keys are AB and BD respectively.

Now this table is already in third normal form but not in BCNF due to the functional dependency D->A.

So we find out the closure of D using the functional dependencies applicable on R and it contains {D,A}.

So we split the table R into two tables: R1(BCD) and R2(AD).

Here, decomposition is lossless. Only the FD D->A is applicable on R2 and the only FD that is applicable for table R! is BD->C since BD is the candidate key. Using these two functional dependencies, there is no way in which we can derive the FD AB->CD. Hence this FD is not applicable on any of the decomposed tables so the BCNF decomposition is not dependency preserving.