\begin{frame} \frametitle{Implication of Functional Dependencies} \vspace{-.5ex} \begin{goal}{} If $A \to B$ and $B \to C$ hold, then $A \to C$ is holds automatically. \end{goal} \vspace{-.5ex} \begin{exampleblock}{} \begin{center} \tableCourses \vspace{-0ex} \end{center} Note that $\sql{courseNr} \to \sql{phone}$ is a consequence of \begin{talign} \sql{courseNr} &\to \sql{instructor} \\ \sql{instructor} &\to \sql{phone} \end{talign} \end{exampleblock} \pause\medskip \begin{goal}{} FDs of the form $A \to A$ always hold. \end{goal} \begin{exampleblock}{} E.g. $\sql{phone} \to \sql{phone}$ holds, but is not interesting \end{exampleblock} \end{frame}