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\begin{frame}
\frametitle{Implication of Functional Dependencies}

\begin{exampleblock}{}
Compute the cover $\{\sql{ISBN}\}^+$ for the following FDs:
\begin{talign}
\sql{ISBN}           & \to \sql{TITLE}, \sql{PUBLISHER} \\
\sql{ISBN}, \sql{NO} & \to \sql{AUTHOR} \\
\sql{PUBLISHER}      & \to \sql{PUB\_URL}
\end{talign}\vspace{-3ex}\pause
\begin{enumerate}
\item We start with $x = \{\sql{ISBN}\}$.
\pause
\item The FD $\sql{ISBN} \to \sql{TITLE}, \sql{PUBLISHER}$ is applicable
since the left-hand side of is completely contained in $x$.
\smallskip\pause

We get $x = \{ \sql{ISBN}, \sql{TITLE}, \sql{PUBLISHER} \}$.
\pause
\item Now the FD $\sql{PUBLISHER} \to \sql{PUB\_URL}$ is applicable.\\
\pause
We get $x = \{\sql{ISBN}, \sql{TITLE}, \sql{PUBLISHER}, \sql{PUB\_URL}\}$.
\pause
\item No further way to extend set $x$, the algorithm returns
\begin{talign}
\{\sql{ISBN}\}^+ = \{\sql{ISBN}, \sql{TITLE}, \sql{PUBLISHER}, \sql{PUB\_URL}\}
\end{talign}
\item \pause We may now conclude, e.g., $\sql{ISBN} \to \sql{PUB\_URL}$.
\end{enumerate}
\end{exampleblock}
\end{frame}