\begin{frame} \frametitle{Splitting Relations: Lossless Splits} \begin{exampleblock}{Lossless split condition satisfied} \recallexamplephone \medskip \pause The lossless split condition is satisfied since \begin{tcenter} $\{ \sql{courseNr}, \sql{title}, \sql{instructor} \} \;\cap\; \{ \sql{instructor}, \sql{phone} \}$ \\ $= \{ \sql{instructor} \} $ \end{tcenter} and $\sql{instructor}$ is a key of the table \sql{Instructors}. \end{exampleblock} \pause \begin{goal}{} All splits initiated by the \emph{table decomposition method} % for transforming relations into BCNF satisfy the condition of the decomposition theorem. \end{goal} It is \emph{always possible} to transform a relation into BCNF by lossless splitting. \end{frame}