% \begin{frame}
%   \frametitle{Summary}
%   
%   \begin{itemize}
%   \item All FDs should be implied by keys (\emph{BCNF}).\\[.5ex]
%   
%     \remark{%
%       Violating FDs indicate the combination of pieces of
%       information which should be stored separately (presence of an
%       embedded function).  This leads to redundancy.
%     }
%   \bigskip
%   
%   \item A relation may be \emph{normalized} by splitting it.
%     \begin{itemize}
%       \item Normalization to BCNF might not preserve FDs.
%       \item Normalization to 3NF preserevs FDs.
%     \end{itemize}
%   \bigskip
%   
%   \item Sometimes it makes sense to avoid a split (violate BCNF).\\[.5ex]
%     
%     \remark{%
%       The DB designer has to carefully resolve such scenarios,
%       incorporating application or domain knowledge.
%     }
%   \end{itemize}
% \end{frame}

\theme{Multivalued Dependencies}