\begin{frame} \frametitle{Introduction} \begin{block}{Recall the Decomposition Theorem} The split of relations is \emph{guaranteed to be lossless} if the intersection (the shared set attributes) of the attributes of the new tables is a key of at least one of them. \end{block} \pause \begin{alertblock}{} The condition in the decomposition theorem is only \begin{itemize} \item \emph{sufficient} (it guarantees losslessness), \item but \emph{not necessary} (a decomposition might be lossless even if the condition is not satisfied). \end{itemize} \end{alertblock} \bigskip \pause \begin{goal}{} \emph{Multivalued dependencies (MVDs)} are constraints that give a \emph{necessary and sufficient} condition for lossless decomposition \end{goal} MVDs lead to the \emph{Fourth Normal Form (4NF)}. \end{frame}