**Puzzle 204.** I would define \$$\Phi\$$ as follows:

- If there are no requirements then the feasibility relation is satisfied no matter how much money we have:

$\Phi(\texttt{false}, y) = \texttt{true}, \mbox{ for all } y \in [0,\infty).$

- If the requirement is to buy a ticket then we need at least \$500 to satisfy the feasibility relation:

$\Phi(\texttt{true}, y) = \begin{cases} \texttt{true} &\mbox{if } 500 \le y \\\\ \texttt{false} & \mbox{otherwise.}\end{cases}$