Please read the question carefully,

Let $M$ be the PDA

$Q=\{q_0,q_1,q_2\}$

$=\{a,b\}$

$=\{A\}$

$F=\{q_2\}$

$$:$(q_0,a,)=\{[q_0,A]\}$

$(q_0,b,A)=\{[q_1,]\}$

$(q_1,b,)=\{[q_2,]\}$

$(q_2,b,A)=\{[q_1,]\}$

a$)$ Draw the state diagram of $M.$

b$)$ Trace the computation of aabbbb in $M.$

c$)$ Give a set$-$theoretic definition of $L(M).$

d$)$ Build a context$-$free grammar $G$ that generates $L(M).$

e$)$ Give the derivation of aabbbb in G$.$