When rolling dice in a board game (like RISK), one might use
\begin{equation*}
S= \text{{ (a,b) : a=die 1 outcome, b=die 2 outcome}}
\end{equation*}
Choose
\begin{equation*}
X( (a,b) ) = \text{max{a,b}}.
\end{equation*}
Then, \(R\) = {1, 2, 3, 4, 5, 6}.