Prove whether the following languages are context$-$free..

a$.L_1=\{ww|win\{0,1{\}}^{**}\}$

b$.L_2=\{\begin{array}{c}{a}^m{b}^n{c}^{p}dqn=q\end{array}$ or $pm$ or $\{$:$m+n=p+q\}$

Write the regular expression that defines the context$-$free language generated by the following grammar $($explaining how you handle each non$-$terminal symbol$)$

$SEE$

$EFE|F|$

$F0F|1F|e.$

Create context$-$free grammars that generate the following languages.

a$.L_3=a^n{b}^m{a}^n,($n$,m1)$

b$.)$

$G=(V,R,R,S)$ grammar is defined as follows:

$V=\{S,A,a,b\},$

${\displaystyle \underset{?}{\overset{?}{}}}=\{a,b\}$ and

$R=\{S$aAa,$Se,S$bAb,$ASS\}$

Examine the above context$-$free grammar and create parse trees for the given strings

a$.bb$

b$.$ baabbb

c$.$ abaabaabbbbbba