\begin{frame} \frametitle{Canonical Set of Functional Dependencies} \begin{exampleblock}{} Consider the relation $R(A,B,C,D,E)$ with FDs \begin{talign} A \to D,E && B \to C && B,C \to D && D \to E \end{talign}\vspace{-2ex} \begin{enumerate} \pause \item Make the right-hand sides singular\pause \begin{talign} A \to D && A \to E && B \to C && B,C \to D && D \to E \end{talign}\vspace{-3ex} \pause \item Minimise left-hand sides\pause \begin{talign} A \to D && A \to E && B \to C && B \to D && D \to E \end{talign} We drop $C$ from $B,C \to D$ since $D \in \{\,B\,\}^+$ due to $B \to C$. \pause \item Remove implied FDs\pause \begin{talign} A \to D && B \to C && B \to D && D \to E \end{talign} $A \to E$ can still be derived from $A \to D$ and $D \to E$. \end{enumerate} \pause\smallskip Thus we have obtained the following \emph{canonical} set of FDs: \begin{talign} A \to D && B \to C && B \to D && D \to E \end{talign} \end{exampleblock} \end{frame}