For the attribute set ABCDEFG, let the MVDs be:
ABCD DEFG
ABCE ABDFG
ABD CDEFG
Find a lossless decomposition into 4NF. Is it unique?
Use the ?rst MVD to obtain the following decomposition: ABCD, DEFG. The second MVD still applies to ABCD and yields ABC, ABD. The third MVD cannot be used to decompose ABC because the join attribute, D, is not in this attribute set. It cannot be used to decompose ABD or DEFG because these sets are subsets of one of the components of that MVD, so the MVD yields trivial decompositions in these cases. Thus, the result is ABC , ABD, DEFG.
The above decomposition is not unique. If we apply the third MVD ?rst, we would obtain the following result: ABD, CD, DEFG.
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