Automata

(10 pt.) In the lecture, we proved that the class of regular languages is closed under complement by showing that if M is a DFA that recognizes a regular language A, then swapping the accepting and non-accepting states yields a DFA M that recognizes the complement of A. Show, by giving a counterexample, that this construction may not work if M is an NFA instead of a DFA. That is, show that if N is an NFA that recognizes a regular language A, then swapping the accepting and non-accepting states may not result in an NFA N that recognizes the complement of A. Justify your answer. Hint: give a specific NFA N=(Q,,,q0,F) for which the constructed NFA N=(Q,,,q0,QF) does not recognize the complement of the language of N