in Databases
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$R(ABCD)$

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

AB and DB  are  candidate key 

in Databases
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4 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
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1 Answer

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Best answer
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.
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