\begin{frame}
  \frametitle{Boyce-Codd Normal Form: Examples}

  \begin{exampleblock}{}
    Consider the relation 
    \begin{center}
      \sql{Product(productNr, name, price)}
    \end{center} 
    and the following FDs:
    \begin{center}
      $
      \begin{array}{rcl}
        \sql{productNr} & \to & \sql{name} \\
        \sql{productNr} & \to & \sql{price} 
      \end{array}
      \qquad
      \begin{array}{rcl}
        \sql{price}, \sql{name} & \to & \sql{name} \\
        \sql{productNr}, \sql{price}   & \to & \sql{name} 
      \end{array}
      $
    \end{center}
    
    Is this relation in BCNF?
    \begin{itemize}
    \pause
      \item Note that $\{\, \sql{productNr} \,\}$ is a key.
    \pause
      \item The FD $\sql{price}, \sql{name} \to \sql{name}$ is trivial.
    \pause
      \item All other FDs are implied by the key $\{\, \sql{productNr} \,\}$.
    \pause
    \end{itemize}
    Thus the relation \sql{Product} \emph{is in BCNF}.
  \end{exampleblock}
\end{frame}