**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} \]

- 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} \]