\begin{frame}
  \frametitle{Determinants}
  
  \begin{block}{Determinants (Non-trivial, minimal FDs)}
    \raggedright
    $\{\, A_1, \dots, A_n \,\}$ is a \emph{determinant} for $\{\, B_1, \dots, B_m \,\}$ if 
    \begin{itemize}
      \item the FD $A_1, \dots, A_n \to B_1, \dots B_m$ holds, and
      \item the \emph{left-hand side is minimal}, that is, if any $A_i$ is removed
        then $A_1, \dots, A_{i-1}, A_{i+1}, A_n \to B_1, \dots B_m$ 
        does \textit{not} hold, and
      \item it is \emph{not trivial}, that is, $\{B_1, \dots, B_m\} \not\subseteq \{A_1, \dots, A_n\}$.
    \end{itemize}
  \end{block}
  (In a canonical set of FDs, all FDs are determinants.)
  \pause
  
  \begin{exampleblock}{}
    \begin{center}
      $
      \mathcal{F} = \left\{
      \begin{array}{rcl}
        \sql{sid}, \sql{exercise} & \to & \sql{points} \\
        \sql{exercise}                 & \to & \sql{maxPoints}
      \end{array} \right\}
      $\vspace{-.5ex}
    \end{center}
    Are the following determinants?
    \begin{itemize}
      \pause
      \item $\sql{points},\; \sql{maxPoints}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause No
      \pause
      \item $\sql{exercise}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause No
      \pause
      \item $\sql{sid},\; \sql{exercise}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause Yes
      \pause
      \item $\sql{exercise},\; \sql{points}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause Yes
    \end{itemize}    
  \end{exampleblock}
\end{frame}