Consider the schema $R(A, B, C, D)$ and the functional dependencies $A \to B$ and $C \to D$. If the decomposition is made as $R_1(A, B)$ and $R_2(C, D)$, then which of the following is TRUE?
- A. Preserves dependency but cannot performs lossless join
- B. Preserves dependency and performs lossless join
- C. Does not preserve dependency and cannot performs lossless join
- D. Does not preserve dependency but performs lossless join
Answer: A. Preserves dependency but cannot performs lossless join
Explanation: Dependencies $A \to B$ (in R1) and $C \to D$ (in R2) are preserved.\nLossless join check: $R_1 \cap R_2 = \phi$. The intersection is empty, so it cannot be a key for either. The join is lossy.