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Consider a schema $R(A,B,C,D)$ and functional dependencies $A \rightarrow B$ and $C \rightarrow D$. Then the decomposition of R into $R_1 (A,B)$ and $R_2(C,D)$ is

- dependency preserving and lossless join
- lossless join but not dependency preserving
- dependency preserving but not lossless join
- not dependency preserving and not lossless join

## 2 Answers

Best answer

### 6 Comments

A decomposition {R1, R2} is a lossless-join decomposition if **R1 ∩ R2 → R1 (R1 should be key) or R1 ∩ R2 → R2 (R2 should be key) **but (A,B) ∩ (C,D) = ∅ so lossy join

FD:1 A→B

FD:2 C→D

R1(A,B) have all attributes of FD1 and R2(C,D) have all attributes of FD2 so ,dependency preserved decompostion

Reference : - question no. 8.1 Korth http://codex.cs.yale.edu/avi/db-book/db6/practice-exer-dir/8s.pdf