$(20$ pts$)$ Construct the complement FA of the following FA

$2.(\backslash (\backslash$mathbf$\{20\}\backslash$mathbf$\{$p t s$\}\backslash ))$ Find the regular expression for the following TG$.$ Show every step of the state elimination process. Do not provide the final regular expression without the step$-$by$-$step explanation.

$3.(\backslash (\backslash$mathbf$\{40\}\backslash$mathbf$\{$~ p t s $)\}\backslash )$ Build the union and the intersection machines for the two following languages described by the two following FAs.

$4.(20$ pts$)$

Prove that the language $\backslash (\backslash$mathrm$\{$L$\}=\backslash$left$\backslash \{\backslash$mathrm$\{$a$\}^\{\backslash$mathrm$\{$n$\}\}\backslash$mathrm$\{$b$\}^\{2\backslash$mathrm$\{$n$\}\}\backslash$right$\backslash \}\backslash )$ is non$-$regular.