\begin{frame}
  \frametitle{ER Models vs. UML Class Diagrams}

  \begin{goal}{Cardinality Limits}
  \begin{minipage}{.49\textwidth}
    \begin{center}
    \scalebox{.92}{\small
    \begin{tikzpicture}[every edge/.style={link},node distance=22mm,>=triangle 45,inner sep=.5mm]
      \begin{scope}
        \node[relationship] (R) {R};
        \node (l) [left of=R,entity] {E1}; \draw (R) -- node[above,pos=.45] {$M_1\sldots M_2$} (l); 
        \node (r) [right of=R,entity] {E2}; \draw (R) -- node[above,pos=.45] {$N_1\sldots N_2$} (r);
      \end{scope}
    \end{tikzpicture}
    }
    \end{center}
  \end{minipage}
  \begin{minipage}{.49\textwidth}
    \begin{center}
    \quad\quad\begin{tikzpicture}[nodes={xscale=.8}]
    \umlclass[width=5mm]{E1}{ 
      \ldots
    }{} 
    \umlclass[x=3.5cm,width=5mm]{E2}{ 
      \ldots
    }{} 
    \umlassoc[arg1=$M_1.. M_2$,pos1=0.2,arg2=$N_1.. N_2$,pos2=.8,name=assoc]{E1}{E2} 
    \node [ao=assoc-1] {R};
    \end{tikzpicture} 
    \end{center}
  \end{minipage}
  \end{goal}
  
  The cardinalities indicate that:
  \begin{itemize}
    \item each E2 entity is related to $\ge M_1$ and $\le M_2$ entities in $E_1$
    \item each E1 entity is related to $\ge N_1$ and $\le N_2$ entities in $E_2$
  \end{itemize}
  \bigskip
  \pause
  
  In UML we have the following abbreviations:
  \begin{itemize}
    \item $1$ stands for $1..1$
    \item $*$ stands for $0..*$
  \end{itemize}
  \begin{goal}{}
    Often better to write fully $1..1$ and $0..*$. 
  \end{goal}
\end{frame}