>**Puzzle 208.** Suppose you some slices of bread, some slices of cheese and some slices of ham. You are trying to make sandwiches. You can make a cheese sandwich with two slices of bread and one slice of cheese. You can make a ham sandwich with two slices of bread and one slice of ham. There is a feasibility relation \\(\Theta : \mathbb{N} \times \mathbb{N} \nrightarrow \mathbb{N} \times \mathbb{N} \times \mathbb{N} \\) where \\(\Theta(m,n,i,j,k) = \text{true}\\) if you can make \\(m\\) cheese sandwiches and \\(n\\) ham sandwiches from \\(i\\) slices of bread, \\(j\\) slices of cheese and \\(k\\) slices of ham.

\[

\Theta(m,n,i,j,k) =

\begin{cases}

\texttt{true} & \mbox{if } m \leq j \mbox{ and } n \leq k \mbox{ and } m+n \leq 4i \\\\

\texttt{false} & \mbox{otherwise.}

\end{cases}

\]

\[

\Theta(m,n,i,j,k) =

\begin{cases}

\texttt{true} & \mbox{if } m \leq j \mbox{ and } n \leq k \mbox{ and } m+n \leq 4i \\\\

\texttt{false} & \mbox{otherwise.}

\end{cases}

\]