Question

- Given R(A,B,C,D) with FDs ={B−>C,D−>A}

- Decompose into BC and AD.
Question: is this decomposition good?

Answer 1

The decomposition of relation R(A,B,C,D) with FDs={B→C,D→A} into BC and AD is not a good decomposition as it does not ensure a lossless-join, meaning it could lead to loss of information and we cannot retrieve the original dataset perfectly.

Step-by-step explanation:

The question is about decomposing a relation R(A,B,C,D) with functional dependencies FDs ={B→C, D→A} into two relations BC and AD. The goal of this decomposition is to check whether it preserves the dependencies and the original data.

To verify if the decomposition is acceptable, we need to perform a lossless-join decomposition, which ensures that the original relation R can be perfectly reconstructed from the decomposed relations BC and AD.

Since B cannot determine A or D from the given FDs and D cannot determine B or C, decomposing R into BC and AD will cause a loss of information as it is not possible to perform a natural join on the relations to retrieve the original relation R. Therefore, this decomposition is not considered good.