We consider regular languages $$over the $2-$element alphabet $\backslash$Sigma $=\{0,1\}.($a$)$ Give two different examples of regular languages $$over $\backslash$Sigma $=\{0,1\}$ whose minimal automaton has exactly three states. For each of your two example languages, give the minimal automaton $($as a diagram$)$ and a regular expression and justify the minimality claim. $($b$)$ Give an example of a nonempty $\{0,1\}$ language that accepts an NFA with fewer than three states but whose minimal automaton has three states. It is sufficient to specify suitable NFA and DFA.