\item \self Find a symbolic binary encoding for
$X = \{ 0,1, \ldots, 31 \}$.
Use it to compute formulas in propositional logic that symbolically represent the following sets. 

\begin{itemize}
  \item $B =\{8, 9, 10, 11, 12, 13, 14, 15\}$
  \item $C =\{x \in X \mid 0 \leq x \leq 15\}$
\end{itemize}

Compute the characteristic functions of the following sets by symbolic operations, using your results from before.
\begin{enumerate}
  \item $D = B \cup C$
  \item $E = B \cap C$
  \item $F = C \setminus B$
\end{enumerate}