Prove that the following languages are context-free by giving grammars that accept them

$\displaystyle \{ ww^R \mid w \in \Sigma^*\}$

I am not sure if this valid, but this is my proof :

The set $\displaystyle S = \{ ww^R \mid w \in \Sigma^*\}$} is context –free. We construct a CFG to prove this proposition.

Let Σ={$\displaystyle {a_1,a_2,$…,$\displaystyle a_n}$}, then the following CFG accepts S.

S→$\displaystyle A_1$ | $\displaystyle A_2 $ |…|$\displaystyle A_n$ | ϵ

$\displaystyle A_1$→$\displaystyle a_1 Ta_1$ | $\displaystyle a_1 a_1$

$\displaystyle A_2$→$\displaystyle a_1 Ta_2$ | $\displaystyle a_2 a_2$

…

$\displaystyle A_n$→$\displaystyle a_n Ta_n$ | $\displaystyle a_n a_n$