Consider the grammar.

SlongrightarrowaSa$|aBa$

BlongrightarrowbB$|lon$

$($a$)$ Give a leftmost derivation of aaaa.

$($b$)$ Give a rightmost derivation of abba.

$($c$)$ Give a rightmost derivation of aabbbbaa.

$($d$)$ Build the derivation trees for parts $($a$),($b$)$ and $($c$).$

$($e$)$ Use set notation to describe the language generated by the grammar.