>**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.

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.