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UGC NET CSE | August 2024 | Part 2 | Question: 30

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Which of the following relations can not be decomposed in to BCNF with a lossless join and dependency-preserving decomposition?

  1. $\mathrm{R}(\mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}, \mathrm{Z})\{\mathrm{VW} \rightarrow \mathrm{X}, \mathrm{WX} \rightarrow \mathrm{V}, \mathrm{VX} \rightarrow \mathrm{W}, \mathrm{W} \rightarrow \mathrm{Y}, \mathrm{Y} \rightarrow \mathrm{Z}\}$
  2. $\mathrm{R}(\mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y})\{\mathrm{VW} \rightarrow \mathrm{W}, \mathrm{X} \rightarrow \mathrm{Y}\}$
  3. $\mathrm{R}(\mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y})\{\mathrm{VW} \rightarrow \mathrm{X}, \mathrm{X} \rightarrow \mathrm{VY}\}$
  4. $\mathrm{R}(\mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}, \mathrm{Z})\{\mathrm{VW} \rightarrow \mathrm{X}, \mathrm{X} \rightarrow \mathrm{Y}, \mathrm{Y} \rightarrow \mathrm{Z}, \mathrm{Z} \rightarrow \mathrm{V}\}$

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