$1$ Context$-$Free Languages

Are the following languages context$-$free or not? If yes, specify a context$-$free

grammar in BNF notation that generates the language. If not, try to give an

informal argument $($proving a language is not context$-$free requires Pumping

Lemma, which is not covered in our class, but if you can learn Pumping

Lemma by yourself and prove it correctly, it will be extra$-$credit$).$

$($a$)\{a^m{c}^o{b}^m|m>0,o>0\},$ with alphabet $=\{a,b,c\}$

$($b$)\{a^n{b}^{3n}|n0\},$ with alphabet $=\{a,b\}$

$($c$)\{\begin{array}{c}w{w}^R|win{}^{**}\end{array}$ and $w^R$ is $w$ in reverse