\item \self Consider the domain $A=\{Asparagus, \;Bell \; Pepper, \;Cabbage, \;Tomato, \\ \; Onion, \;Zucchini, \;Eggplant, \; Mushroom\}$ and
    the two different symbolic encodings for $A$ given below.
    Which one gives a shorter characteristic function for the following sets?
    \begin{enumerate}
	     \item $B = \{Asparagus, \; Mushroom\}$
        \item $C = \{Bell \; Pepper, \; Onion, \; Zucchini, \; Eggplant\}$
        \item $D = \{Cabbage, \; Tomato\}$
   \end{enumerate}
    Illustrate your answer by giving the
    characteristic function for $B$, $C$ and $D$ in both encodings.

\vspace{.5cm}

%\begin{minipage}
    \begin{tabular}{l|l|l|l}
    \hline
    \multicolumn{3}{c}{\textbf{Encoding 1}} \\
    \hline
    Element & x & y & z\\
    \hline
    Asparagus & $0$ & $0$ & $0$ \\
    Bell Pepper & $0$ & $0$ & $1$ \\
    Cabbage & $0$ & $1$ & $0$ \\
    Tomato & $0$ & $1$ & $1$  \\
    Onion & $1$ & $0$ & $0$ \\
    Zucchini & $1$ & $0$ & $1$  \\
    Eggplant & $1$ & $1$ & $0$ \\
    Mushroom & $1$ & $1$ & $1$
   \end{tabular}
%\end{minipage}
%\begin{minipage}
\hspace{3cm}
   \begin{tabular}{l|l|l|l}
    \hline
    \multicolumn{3}{c}{\textbf{Encoding 2}} \\
    \hline
    Element & x & y & z \\
    \hline
    Asparagus & $1$ & $1$ & $0$ \\
    Bell Pepper & $1$ & $0$ & $1$ \\
    Cabbage & $0$ & $1$ & $0$ \\
    Tomato & $1$ & $1$ & $1$  \\
    Onion & $0$ & $0$ & $0$ \\
    Zucchini & $0$ & $0$ & $1$  \\
    Eggplant & $1$ & $0$ & $0$ \\
    Mushroom & $0$ & $1$ & $1$
   \end{tabular}
%\end{minipage}
