This exercise relies on a technique explained in the optional Section 6.10. Consider a relation schema over the attributes ABCDEFGHI and the following MVDs and FDs:
Find a lossless and dependency-preserving decomposition into 4NF.
The ?rst step is to close the left-hand sides of the MVDs with respect to the FDs:
The 4NF decomposition algorithm ?rst yields ABCDH , ADHEFGI .Then ABCDH is split into CB, CADH . ADHEFGI is split by the third MVD into GIAE, GIDHF . Thus, after the 4NF decomposition stage we get: CB, CADH , GIAE, GIDHF .
The last three schemas are not in 3NF, due to the FDs. A lossless, dependency preserving 3NF decomposition of CADH is DAH , DC. A 3NF decomposition of GIAE is GI , GAE, and A 3NF decomposition of GIDHF is DH , GI , DGF .SinceDAH and DH have the same key, we can eliminateDH and obtain the following ?nal result: CB, DC , DAH , GI , GAE, DGF.
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