let R (A, B, C, D) be a relational schema with following function dependencies:
A → B, B → C
C → D and D → B
The decomposition of R into
(A, B) (B, C) (B, D)
1
gives a lossless join, and is dependency preserving
2
gives lossless join, but is not dependency preserving
3
does not give a lossless join, but is dependency preserving
4
does not give a lossless join and is not dependency preserving