Question 26

The initial state is $\{q_0\}$.

1. Input symbol '0':

   • From $q_0$, on '0' there is only a self-loop back to $q_0$.
   • Set of reachable states: $\{q_0\}$.

2. Input symbol '0':

   • From $q_0$, on '0' self-loop stays at $q_0$.
   • Set of reachable states: $\{q_0\}$.

3. Input symbol '1':

   • From $q_0$, on '1' the automaton can take the self-loop back to $q_0$, or take the transition to $q_1$.
   • Set of reachable states: $\{q_0, q_1\}$.

4. Input symbol '1':

   • From $q_0$, on '1' can go to $q_0$ (self-loop) or $q_1$ (transition).
   • From $q_1$, on '1' transitions to $q_2$.
   • Union of reachable states: $\{q_0, q_1, q_2\}$.

Note that $q_3$ is not reachable because reaching $q_3$ from $q_2$ requires an input transition after being in $q_2$.

Thus, the set of reachable states is $\{q_0, q_1, q_2\}$.