$2$ points Prove the language L $=\{$w in $\{$a$,$ b$\}|$ na$($w$)>$ nb$($w$)\}$ is not

a regular language.

$6$ points Consider the following context$-$free grammar G$.$

S $->$ aXbb $|$ bY cc $|$ SS $|\backslash$epsi

X $->$ aXbb $|\backslash$epsi

Y $->$ bY cc $|\backslash$epsi

Show how to derive the string bccaabbbb in G$.$ Using grafstate, provide

the step$-$by$-$step derivation and a parse tree.