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\begin{frame}
\frametitle{Cardinality Limits: Many-to-Many}

\begin{center}
\begin{scope}
\node[relationship] (R) {R};
\node (l) [left of=R,entity,minimum size=4mm] {A}; \draw (R) -- node[above,pos=.6] {$0\sldots *$} (l);
\node (r) [right of=R,entity,minimum size=4mm] {B}; \draw (R) -- node[above,pos=.6] {$0\sldots *$} (r);

\begin{scope}[nodes={draw,rectangle,fill=green!20,minimum size=4mm,scale=.8}]
\foreach \i in {1,2,3,4,5,6,7} {
\node at (-12mm,-5mm*\i - 4mm) (a\i) {a\i};
\node at (12mm,-5mm*\i - 4mm) (b\i) {b\i};
}
\end{scope}

\begin{scope}[thick]
\draw (a1) to[out=0,in=180] (b1);
\draw (a3) to[out=0,in=180] (b2);
\draw (a4) to[out=0,in=180] (b3);
\draw (a4) to[out=0,in=180] (b5);
\draw (a4) to[out=0,in=180] (b6);
\draw (a5) to[out=0,in=180] (b6);
\draw (a6) to[out=0,in=180] (b6);
\draw (a6) to[out=0,in=180] (b7);
\end{scope}
\end{scope}
\end{tikzpicture}\vspace{-.5ex}
\end{center}

\begin{goal}{}
This describes a \emph{many-to-many} relationship set:
\begin{itemize}
\item the entities may be connected arbitrarily
\item every $a$ in $A$ can be linked to an arbitrary number of $B$'s
\item every $b$ in $B$ can be linked to an arbitrary number of $A$'s
\end{itemize}
\end{goal}
If the cardinalities are not given, the \emph{default is many-to-many}.
\vspace{10cm}
\end{frame}