Consider a decomposition R 1 ,...,R of R obtained through 3NF synthesis. Suppose that Ri is not in BCNF and let X ? A be a violating FD in Ri. Prove that Ri must have another FD, Y ? B, which will be lost if Ri is further decomposed with respect to X ? A.
What will be an ideal response?
If X ? A is a violating FD of Ri, there must be a key K in Ri and an FDK ? B in the minimal cover, such that A ? K , X ? K ,and B ? K. Since the decomposition with respect to X ? A splits the attributes of K between the schemas XA and Ri ? A, where Ri is the set of attributes of Ri, the FDK ? B is not embedded in any schema.
If it were possible to derive K ? B using the remaining FDs, then it would mean that K ? B is redundant, contrary to the fact that it was chosen from a minimal cover.
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What will be an ideal response?
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