1. **Problem Statement:** Determine if the strings "ababbaaa" and "abaa" are accepted or rejected by the given automata A, B, and C. 2. **Understanding the Automata:** Each automaton has states and transitions labeled with letters a and b. A string is accepted if there exists a path from the start state to a final state following the string's letters. 3. **Assumptions:** Since final states are not explicitly given, we assume all states are accepting states for this problem or that acceptance depends on reachability. 4. **Check String I: "ababbaaa"** - For Automaton A: - Start at state 1. - Read 'a': 1 → 2 (a) - Read 'b': 2 → 3 (b) - Read 'a': 3 has no outgoing 'a' edge, but from 2 → 4 (a,b) and 4 → 3 (a), so try 2 → 4 → 3 path. - However, after reading 'b' at 2 → 3, no 'a' from 3. - Try alternative path: 1 → 4 (a,b) on 'a', then 4 → 3 (a) on 'a'. - The string does not fit the transitions exactly; thus, likely rejected. - For Automaton B: - Start at 1. - 'a': 1 → 2 (a,b) - 'b': 2 → 4 (a) - 'a': 4 → 2 (a) - 'b': 2 → 4 (a) - 'b': 4 → 2 (a) - 'a': 2 → 4 (a) - 'a': 4 → 2 (a) - 'a': 2 → 4 (a) - The string can be followed by alternating between 2 and 4 states. - Accepted. - For Automaton C: - Start at 1. - 'a': 1 → 2 (a,b) - 'b': 2 → 5 (a,b) - 'a': 5 → 6 (a,b) - 'b': 6 has no outgoing edges. - String cannot be fully processed. - Rejected. 5. **Check String II: "abaa"** - Automaton A: - 1 → 2 (a) - 2 → 3 (b) - 3 no 'a' edge, but 1 → 4 (a,b) and 4 → 3 (a) exist. - String does not fit transitions fully. - Rejected. - Automaton B: - 1 → 2 (a,b) - 2 → 4 (a) - 4 → 2 (a) - 2 → 4 (a) - Accepted. - Automaton C: - 1 → 2 (a,b) - 2 → 3 (a) - 3 → 6 (a,b) - 6 no outgoing edges for next 'a'. - Rejected. **Final answers:** - String "ababbaaa": Accepted by B, Rejected by A and C. - String "abaa": Accepted by B, Rejected by A and C.