Let R (A, B, C, D) be a relational schema with the following functional dependencies:
A → B, B → C,
C → D and D → B.
The decomposition of R into
(A, B), (B, C), (B, D)
gives a lossless join, and is dependency preserving
gives a lossless join, but is not dependency preserving
does not give a lossless join, but is dependency preserving
does not give a lossless join and is not dependency preserving
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Gate IT 2008