\item \self Given a state space of size $|S| = 16$, find a symbolic binary encoding for this state space and compute the characteristic function for the sets of states $$C = \{s_{0}, s_{2}, s_{8}, s_{10}\} \enspace \text{and} \enspace C = \{s_{0}, s_{2}, s_{8}, s_{10}\}$$ Then compute the characteristic function for the sets $D = C \subseteq B$, $E = B \setminus C$ and $F = S \setminus E$. If possible, simplify the formulas.