a$)$ If $L$ is a regular language, prove that the language $\{\begin{array}{c}uv\text{:}\text{u}\text{i}\text{n}\text{L}\\ vin{L}^R\end{array}$ is also

regular.

b$)$ Show that language $L=\{a^n{b}^{2n}$:$n0\}$ is not a regular language $($using the

pumping lemma$).$