Find regular grammars for the following languages on {$ a, b$}.
(a) $L=${$w:n_a(w)$ and $n_b(w)$ are both even}.
(b) $L=${$w:(n_a(w)$ - $n_b(w))$ mod $3=1$}.
(c) $L=${$w:(n_a(w)$ - $n_b(w))$ mod $3\neq1$}.
(d) $L=${$w:(n_a(w)$ - $n_b(w))$ mod $3\neq0$}.
(e) $L=${$w:|n_a(w)$ - $n_b(w)|$ is odd}.
