Consider the following statements:
$L_1=\left\{\text{wxw$^R$|w$\in$(a,b)$^*$, x$\in$c }\right\}$
$L_2=\left\{\text{wy|w, y $\in$ (a,b)$^*$}\right\} $
$L_3=\left\{\text{zwz|w$\in$(a,b)$^*$,Z$\in$}\left\{a\right\} \right\}$
$L_4=\left\{\text{wxw|w $\in$ (a,b)$^*$, x$\in$} \left\{c\right\}^* \right\}$
Which of the following statements are $\text{CORRECT}$?
- All languages $L_1, L_2, L_3, L_4$ are context free languages
- Languages $L_1, L_3$ are context free language and $L_2, L_4$ are regular
- $L_1$ is context free, $L_2$ and $L_3$ are regular and $L_4$ is context sensitive languages
- $L_1, L_4$ are context free, $L_2$ and $L_3$ is context sensitive languages