1. The problem is to draw an NFA that recognizes the language $L = \{ x \in \{a,b\}^* \mid x \text{ contains } aa \text{ as a substring} \}$. This means any string over the alphabet $\{a,b\}$ that has two consecutive $a$s somewhere inside it. 2. To design this NFA, we use states to track whether we have seen an $a$ and then another $a$ immediately after. 3. The NFA has three states: - $q_0$: the start state, where we have not seen any $a$ yet. - $q_1$: we have seen one $a$ and are waiting to see if the next character is also $a$. - $q_2$: the accept state, meaning we have seen $aa$ as a substring. 4. The transitions are: - From $q_0$, on input $a$, go to $q_1$ (we saw the first $a$). - From $q_0$, on input $b$, stay in $q_0$ (no $a$ seen yet). - From $q_1$, on input $a$, go to $q_2$ (we saw $aa$). - From $q_1$, on input $b$, go back to $q_0$ (the substring $aa$ was broken). - From $q_2$, on input $a$ or $b$, stay in $q_2$ (once accepted, remain accepted). 5. This NFA accepts exactly those strings that contain $aa$ as a substring. Since the user requested only the first problem solved, this completes the answer.