$[30$ 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 $=\{$wuwR $|$ w$,$ u in $($a $+$ b$)$

$\}$

ii$)$ L $=\{$wuwR $|$ w$,$ u in $($a $+$ b$)$

$$ and $|$w$|=|$u$|\}$

iii$)$ L $=\{$w$1$cw$2|$ w$1=$ w$2$

R and w$1,$ w$2$ in $($a $+$ b$)$

$\}$