7.17

Give an example of a relation schema \(R'\) and set \(F'\) of functional dependencies such that there are at least three distinct lossless decompositions of \(R'\) into BCNF.

---

Given the relation \(R' = (A, B, C, D)\) the set of functional dependencies \(F' = A \rightarrow B, C \rightarrow D, B \rightarrow C\) allows three distinct BCNF decompositions.

\[R_1 = \{ (A, B), (C, D), (B, C) \}\] is in BCNF as is \[R_2 = \{ (A, B), (C, D), (A, C) \}\] \[R_3 = \{ (B, C), (A, D), (A, B) \}\]