\begin{frame} \frametitle{Covers} \begin{exampleblock}{} Consider the following set $\mathcal{F}$ of FDs: \begin{enumerate} \item $\sql{isbn} \to \sql{title}, \sql{publisher}$ \item $\sql{isbn}, \sql{no} \to \sql{author}$ \item $\sql{publisher} \to \sql{publisherURL}$ \end{enumerate} Compute the cover $\{\sql{isbn}\}_{\mathcal{F}}^+$: \begin{itemize} \pause \item We start with $x = \{\sql{\,isbn\,}\}$. \pause \item FD $1$ is applicable since $\{\sql{\,isbn\,}\} \subseteq x$.\\[.5ex] \pause We get $x = \{\, \sql{isbn}, \sql{title}, \sql{publisher} \,\}$. \pause \item FD $3$ is applicable since $\{\sql{\,publisher\,}\} \subseteq x$.\\[.5ex] \pause We get $x = \{\, \sql{isbn}, \sql{title}, \sql{publisher}, \sql{publisherURL} \,\}$. \pause \end{itemize} No further way to extend set $x$, thus \begin{talign} \{\sql{isbn}\}_{\mathcal{F}}^+ \;=\; \{\, \sql{isbn}, \sql{title}, \sql{publisher}, \sql{publisherURL} \,\} \end{talign} \pause We may now conclude, e.g., $\sql{isbn} \to \sql{publisherURL}$. \end{exampleblock} \end{frame}