\begin{frame} \frametitle{Canonical Set of Functional Dependencies} \begin{exampleblock}{} Compute the canonical set of FDs for \vspace{-.5ex} \begin{talign} A,B,C &\to D,E & B &\to C & B &\to E & C &\to E & C,D &\to D,F \end{talign}\vspace{-3ex} \begin{enumerate} \pause \item Make the right-hand sides singular\pause\vspace{-.5ex} \begin{talign} A,B,C &\to D & B &\to C & B &\to E & C &\to E & C,D &\to D \\[-.5ex] A,B,C &\to E & &&&&&& C,D &\to F \end{talign}\vspace{-3ex} \pause \item Removing implied FDs:\pause\vspace{-.5ex} \begin{talign} A,B,C &\to E & B &\to E & C,D &\to D \end{talign} This results in \vspace{-.5ex} \begin{talign} A,B,C &\to D & B &\to C & C &\to E & C,D &\to F \end{talign}\vspace{-3ex} \pause \item Minimise left-hand sides\pause\vspace{-.5ex} \begin{talign} A,B &\to D & B &\to C & C &\to E & C,D &\to F \end{talign} We drop $C$ from $A,B,C \to D$ since $D \in \{\, A,B \,\}^+$. \smallskip \end{enumerate} \pause There is nothing more that can be removed. % A,B -> D; B -> C; C -> E; C,D -> F \end{exampleblock} \end{frame}