5. This is based on a past exam question.
Consider the following Nondeterministic Finite Automaton. We will build up a proof, by induction on \( n \), that
for all \( n \), the string (bbba) \( { }^{n} \) is accepted by this NFA.
(a) If the NFA is in state 1 , what states can it be in after reading bbba?
(b) If the NFA is in state 3 and it then reads bbba, what states can it be in when it finishes reading that string?
(c) Is the string bbba accepted by the NFA? Why or why not?
Let \( n \geq 1 \).
(d) Suppose the string (bbba) \( { }^{n} \) is accepted by the NFA. What happens to the string (bbba) \( { }^{n+1} \), i.e., does the NFA accept or reject it? Why?
(e) Explain how to put (some of) your answers together to make a proof by induction of (*).