\item \lect Consider the domain $A=\{Maths, \;English, \;Biology, \;Physical \; Education\}$ and
    the two different symbolic encodings for $A$ given below.
    Which one gives a shorter characteristic function for the following sets?
    \begin{enumerate}
	     \item $B = \{Maths, \; Biology\}$
        \item $C = \{English, \; Biology\}$
        \item $D = \{Maths, \;Physical \; Education\}$
   \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}
    \hline
    \multicolumn{3}{c}{\textbf{Encoding 1}} \\
    \hline
    Element & x & y \\
    \hline
    Maths & $0$ & $0$ \\
    English & $1$ & $0$ \\
    Biology & $0$ & $1$ \\
    Physical Education & $1$ & $1$
   \end{tabular}
%\end{minipage}
%\begin{minipage}
\hspace{3cm}
   \begin{tabular}{l|l|l}
    \hline
    \multicolumn{3}{c}{\textbf{Encoding 2}} \\
    \hline
    Element & x & y \\
    \hline
    Maths & $0$ & $0$ \\
    English & $1$ & $0$ \\
    Biology & $1$ & $1$ \\
    Physical Education & $0$ & $1$
   \end{tabular}
%\end{minipage}