\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 $B =\{x \in X \mid \text{x is even}\}$
  \item $C =\{x \in X \mid \text{x is odd}\}$
  \item $D =\{0,1,2,3,4,5,6,7\}$
\end{itemize}

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