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\item \lect
Find a symbolic binary encoding for $X = \{ 0,1, \ldots, 31 \}$.
Use it to find formulas that symbolically represent the sets $A$ and $B$ and simplify the formulas:
\begin{itemize}
\item $A =\{ 12, 13, 14, 15, 28, 29, 30, 31 \}$
\item $B =\{x \in X \mid 0 \leq x \leq 15\}$
\end{itemize}
Furthermore, give the formulas representing the sets
$C=A\cap B$ and $D = A \cup B$.