Is L' context free language? Given context free grammar :   G=(V,T,P,S).
and  L'={a $\in$ (V $\cup$T)* | S$\Rightarrow$*a}   when $\Sigma$=V $\cup$ T
Is L' context free language ?
I think no because for the grammer:
G=(S,{a,b},P,S)   ,P={ S$\rightarrow$aSb|ab}
we will get that L' is:
L'={$a^nS^nb^n$}$\cup${$a^nb^n$} and L'  is not context free language.

Given context-free grammar $G = (V, T, P, S)$, define $G' = (V, T \cup V', P \cup P', S)$, such that $V'$ has one element for each element of $V$,
$$ V' = \{ v' \mid v \in V \} \enspace, $$
and, for each element $v \in V$, $P'$ contains the production $v \rightarrow v'$.  The language of $G'$ is context-free, and is isomorphic to $L'$.
