Consider a schema R (A, B, C, D) and functional dependencies A → B, C → D. Then, the decomposition of R into R1 and R2 where R1 (AB) and R2 (CD), is -
Asked in Programmer Exam 2024 · Topic: Basics of Computers and Information Technology (Database Management Systems (DBMS) Basics: Concepts, Types of Databases)
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Answer: D. Dependency preserving and lossless join
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- Dependency Preservation A decomposition is dependency preserving if all original functional dependencies can be enforced on the decomposed relations. In this case, $A \rightarrow B$ is preserved in $R_1(AB)$, and $C \rightarrow D$ is preserved in $R_2(CD)$. 2. Lossless Join A decomposition is lossless if the original relation R can be perfectly reconstructed by joining the decomposed relations. A common condition for lossless join decomposition of R into $R_1$ and $R_2$ is that $R_1 \cap R_2$ must contain a superkey for $R_1$ or $R_2$. However, in cases where the dependencies are disjoint and correspond directly to the decomposed relations (as here), the decomposition is typically lossless even if the intersection is empty. The original relation R is effectively the Cartesian product of its projections onto the disjoint attribute sets, which is what $R_1 \bowtie R_2$ would represent in this case. 197. Consider following two instances of relation Student and Faculty with operation on these instances – Student Faculty (a) Student - Faculty (b) (Student ∩ Faculty) U (Faculty ∩ Student) (c) (Student U Faculty) - (Student ∩ Faculty) (d) Student ∩ Faculty Identify the correct option that produces equivalent output -
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