\begin{frame}[t] \frametitle{Cardinality Limits: One-to-One} \begin{center}\vspace{-1ex} \begin{tikzpicture}[every edge/.style={link},node distance=22mm,>=triangle 45] \begin{scope} \node[relationship] (R) {R}; \node (l) [left of=R,entity,minimum size=4mm] {A}; \draw (R) -- node[above,pos=.6] {$1\sldots 1$} (l); \node (r) [right of=R,entity,minimum size=4mm] {B}; \draw (R) -- node[above,pos=.6] {$1\sldots 1$} (r); \begin{scope}[nodes={draw,rectangle,fill=green!20,minimum size=4mm,scale=.8}] \foreach \i in {1,2,3,4,5,6} { \node at (-12mm,-5mm*\i - 3mm) (a\i) {a\i}; \node at (12mm,-5mm*\i - 3mm) (b\i) {b\i}; } \end{scope} \begin{scope}[thick] \draw (a1) to[out=0,in=180] (b1); \draw (a2) to[out=0,in=180] (b3); \draw (a3) to[out=0,in=180] (b2); \draw (a4) to[out=0,in=180] (b6); \draw (a5) to[out=0,in=180] (b4); \draw (a6) to[out=0,in=180] (b5); \end{scope} \end{scope} \end{tikzpicture}\vspace{-.5ex} \end{center} \bigskip \begin{goal}{} This describes a \emph{one-to-one} relationship set: \begin{itemize} \item every $a$ in $A$ is connected to precisely one $b$ in $B$ \item every $b$ in $B$ is connected to precisely one $a$ in $A$ \end{itemize} \end{goal} Note that this corresponds to a bijective function from $A$ to $B$. \end{frame}