Which statement about decomposing a relation is always true?
Correct answer A. A lossless, dependency-preserving decomposition into 3NF always exists
Explanation
The 3NF synthesis algorithm always produces a decomposition that is both lossless-join and dependency-preserving. BCNF guarantees losslessness, but some relations cannot be put into BCNF without losing a dependency; R(A,B,C) with AB -> C and C -> B is the textbook case. Lossless join and dependency preservation are independent properties, so one does not imply the other. This trade-off is why designers sometimes settle for 3NF.
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