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48 lines
1.5 KiB
48 lines
1.5 KiB
\item \self Consider the domain $A=\{Asparagus, \;Bell \; Pepper, \;Cabbage, \;Tomato, \\ \; Onion, \;Zucchini, \;Eggplant, \; Mushroom\}$ and
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the two different symbolic encodings for $A$ given below.
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Which one gives a shorter characteristic function for the following sets?
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\begin{enumerate}
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\item $B = \{Asparagus, \; Mushroom\}$
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\item $C = \{Bell \; Pepper, \; Onion, \; Zucchini, \; Eggplant\}$
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\item $D = \{Cabbage, \; Tomato\}$
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\end{enumerate}
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Illustrate your answer by giving the
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characteristic function for $B$, $C$ and $D$ in both encodings.
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\vspace{.5cm}
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%\begin{minipage}
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\begin{tabular}{l|l|l|l}
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\hline
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\multicolumn{3}{c}{\textbf{Encoding 1}} \\
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\hline
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Element & x & y & z\\
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\hline
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Asparagus & $0$ & $0$ & $0$ \\
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Bell Pepper & $0$ & $0$ & $1$ \\
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Cabbage & $0$ & $1$ & $0$ \\
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Tomato & $0$ & $1$ & $1$ \\
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Onion & $1$ & $0$ & $0$ \\
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Zucchini & $1$ & $0$ & $1$ \\
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Eggplant & $1$ & $1$ & $0$ \\
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Mushroom & $1$ & $1$ & $1$
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\end{tabular}
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%\end{minipage}
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%\begin{minipage}
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\hspace{3cm}
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\begin{tabular}{l|l|l|l}
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\hline
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\multicolumn{3}{c}{\textbf{Encoding 2}} \\
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\hline
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Element & x & y & z \\
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\hline
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Asparagus & $1$ & $1$ & $0$ \\
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Bell Pepper & $1$ & $0$ & $1$ \\
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Cabbage & $0$ & $1$ & $0$ \\
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Tomato & $1$ & $1$ & $1$ \\
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Onion & $0$ & $0$ & $0$ \\
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Zucchini & $0$ & $0$ & $1$ \\
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Eggplant & $1$ & $0$ & $0$ \\
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Mushroom & $0$ & $1$ & $1$
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\end{tabular}
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%\end{minipage}
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