We can express \\(\Phi\\) as a matrix where the \\( (m, n)^{th} \\)
entry is the value of \\( \Phi(m, n) \in \mathbb{B} \\) .
Fill out the \\(\textbf{Bool}\\)-matrix:

\[
\begin{array}{c | c c c c c}
\Phi & a & b & c & d & e \\\\
\hline
N & ? & ? & ? & ? & true \\\\
E & true & ? & ? & ? & ? \\\\
W & ? & ? & ? & false & ? \\\\
S & ? & ? & ? & ? & ?
\end{array}
\]

We’ll call this the feasibility matrix of \\(\Phi\\).

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\[ \textbf{Bool}\text{-profunctor } \Phi : X \nrightarrow Y \]

![drawing](https://docs.google.com/drawings/d/e/2PACX-1vTAo-EOO8mPVKTtHoAXXACqAE7a8FvjYQCfNS2dNRyTrEJlX1cOvMK5FjjHMHtHrDX642MM-0Mk5635/pub?w=639&h=308)