\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 $D = A \cup B$.