theory of computation

1) Show that if M is a DFA that recognizes language B, then swapping the accept and nonaccept states in M yields a new DFA M0 recognizing the complement of B, B. Which operation does this imply the regular languages are closed under?

2) Prove by counterexample that if M is a NFA that recognizes languages B, then swapping the accept and nonaccept states in M does not necessarily yield an NFA recognizing B. With this in mind, is the class of languages recognized by NFAs closed under complement? Explain.