>**Puzzle 204.** Suppose you are trying to buy a plane ticket, and the cheapest available ticket is $500. Describe this using a feasibility relation \$$\Phi : \textbf{Bool} \nrightarrow [0,\infty) \$$ where we make \$$[0,\infty) \$$, the set of nonnegative real numbers, into a poset with its usual ordering \$$\le\$$. This is a feasibility relation \$$\Phi\$$, where \$$\texttt{false}\$$ maps to everything less than$500, and \$$\texttt{true}\$$ maps to everything greater than or equal to $500, ie if you can buy a ticket, then you have at least$500. Since this is required to only be a feasibility relation and not a monotone map, this is a perfectly reasonable thing to do.