Each of the following languages is the complement of a simpler language. In each part, construct a DFA for the simpler language, then use it to give the state diagram of a DFA for the language given. In all parts, Σ = {a, b}.

^Aa. {w| w does not contain the substring ab}

^Ab. {w| w does not contain the substring baba}

c. {w| w contains neither the substrings ab nor ba}

d. {w| w is any string not in a*b*}

e. {w| w is any string not in (ab*)*}

f. {w| w is any string not in a* ∪ b*}

g. {w| w is any string that doesn’t contain exactly two a’s}

h. {w| w is any string except a and b}