Let R(A, B, C, D) be a relational schema with dependencies A → B, B → C, C → D and D → B. The decomposition of R into (A, B), (B, C), (B, D):

1. Agives a lossless join, and is dependency preserving
2. Bgives lossless join, but is not dependency preserving
3. Cdoes not give a lossless join, but is dependency preserving
4. Ddoes not give a lossless join and is not dependency preserving

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. gives a lossless join, and is dependency preserving

Explanation

Lossless: AB and BC share B with B → C; ABC and BD share B with B → D (via C). Dependencies: A → B is in AB, B → C in BC, D → B in BD, and C → D follows from C → B (in BC) and B → D (in BD). Lossless and dependency preserving.