Question $8$ The following question is given: Use the Pumping Lemma with length to prove that the following language is nonregular: The following question is given: Use the Pumping Lemma with length to prove that the following language is nonregular: L$=\{$b a b$^$n$-2$ a$^$n$,$ with n in $\{3,4,5,...\},$ n in Z$\}.$ The solution to this question is partly given as follows: Assume L$=\{$b a b$^$n$-2$ a$^$n$.,$ where $.$n in $\{3,4,5,...\},$ n in Z$\}$ is regular. Then there exists an FA with, say k states that accepts L$.$ Let w$=$b a b$^$k$-2$ a$^$k be a word in L$.$ According to the pumping lemma, w may be written as $[$ w$=$x y z such that; length $($x$)+$ length $($y$)<=$ k AND length $($y$)>0]$ Which one of the following is not one of the possible correct choices for y $?1.$ y comprises the a in between b and b$^$k$-2.2.$ y comprises the first ba$-$substring. $3.$ y comprises ba followed by possible b$\text{'}$s$.4.$ y comprises ba followed by a possible second ba substring.