DFAs and NFAs, pumping lemma, and regular expressions. please help with these provlems.

Let {} (recall that = ). Prove that there is a DFA M having n accepting states that accepts L. (Assume an underlying alphabet of = {1}.) Then prove that L cannot be accepted by any DFA having fewer accepting states.

Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, and complement.

Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, and complement.

(w/w {0, 1)s is not a palindrome)s