Consider the finite automaton in the following figure. What is the set of reachable states for the input string 0011?

We can trace the set of reachable states step-by-step starting from the initial state $q_0$ with the input string $0011$:

1. Initial state:$\{q_0\}$

2. On first input symbol '0':

   $$\delta(q_0, 0) = \{q_0\}$$

   Set of states = $\{q_0\}$

3. On second input symbol '0':

   $$\delta(q_0, 0) = \{q_0\}$$

   Set of states = $\{q_0\}$

4. On third input symbol '1':

   $$\delta(q_0, 1) = \{q_0, q_1\}$$

   Set of states = $\{q_0, q_1\}$

5. On fourth input symbol '1':

   $$\delta(q_0, 1) \cup \delta(q_1, 1) = \{q_0, q_1\} \cup \{q_2\} = \{q_0, q_1, q_2\}$$

Thus, the set of reachable states is $\{q_0, q_1, q_2\}$, which corresponds to option (A).