Consider the grammer $G=(V,,R,S)$ where

$V=\{S,A\}$

$=\{a,b\}$

$R=\{[SlongrightarrowAA,$

Alongrightarrowa,

AlongrightarrowbA,

AlongrightarrowAb$]\}$

$($a$)$ List all strings of $L(G)$ which can be produced by derivations of four or fewer

steps. That is$,$ beginning with $S,$ counting each replacement of one variable with

the right$-$hand side of a rule as one step, find all the strings consisting of only

terminals $($characters from $)$ that can be generated by $G.$

$($b$)$ Give four distinct derivations for the string babbab.

$($c$)$ For any $m,n,p0,$ describe a derivation in $G$ of the string $b^{m}a{b}^{n}a{b}^p.$