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\item \self Find a symbolic binary encoding for $X = \{ 0,1, \ldots, 31 \}$. Use it to find characteristic functions for the following sets. If possible, simplify the formulas.
\begin{enumerate} \item $B =\{x \in X \mid 24 \leq x < 32\}$ \item $C = \left\{ x \in X \middle| \enspace
\begin{array}{lll} 4 & \leq \enspace x & < 8 \\ 12 & \leq \enspace x & < 16 \\ 20 & \leq \enspace x & < 24 \end{array} \right\}$
\end{enumerate} Compute the characteristic functions of the following sets by symbolic operations, using your results from before and simplify your formulas. \begin{enumerate} \item $D = B \cup C$ \item $E = B \cap C$ \end{enumerate}
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