$2\mathrm{.}9$ & $2\mathrm{.}10$ modified$)$ Consider the language

A $=\{$a

i

b

j

c

k

$|$ i $=$ j or j $=$ k where i$,$ j$,$ k $>=0\}.$

$($a$)$ Give a context$-$free grammar that generates A$.$

$($b$)$ Is your grammar from $($a$)$ ambiguous? Why or why not?

$($c$)$ Give a state diagram of a PDA that recognizes A