Q $1.[30$ Points$]$ Classify the following languages into one of the three categories a$)$ regular,

b$)$ context$-$free but not regular, and c$)$ not context$-$free. Note that in$-$order to show that a

language is context$-$free but not regular, you need to prove both that it is context$-$free and

also that it is not regular.

i$)L=\{wu{w}^R|w,$uin$(a+b{)}^{***}\}$

ii$)L=\{\begin{array}{c}wu{w}^R|w\\ \text{u}\text{i}\text{n}& (a+b{)}^{***}\end{array}$ and $\{$:$|w|=|u|\}$

iii$)L=\{\begin{array}{c}{w}_{1}c{w}_2|w_1{w}_2^R\end{array}$ and $\{$:$w_1,w_{2}in(a+b{)}^{***}\}$

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