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, $2=\{$a$,$ b$\}.$a$.\{$w$|$w does not contain the substring ab$\}$b$.\{$of$|$ w does not contain the substring baba$)$c$.$ w w contains neither the substrings ab nor ba$\}$d$.$ fw$|$w is any string not in a$"$b$*\}$