$1.($GRADED $4$ points$)=\{$a$,$b$\}$ Construct a dfa for the following language and also construct a dfa for

the compliment of that language: L $=$ L$($ab$$ baa$)$

$($PRACTICE QUESTION$)**$ Let L$1=$ L$($ab$*$aa$),$ L$2=$ L$($a$*$bba$*).$

Find a regular expression for $($L$1$ L$2)*$ L$2.$

$2.($GRADED $3$ points$)=\{$a$,$b$\}$Construction technique for compliment

Describe the construction technique that is used for the following:

From a dfa that has been constructed for language L$,$ L$(($a$*($ba $+$ b$))$

how would one construct the dfa for $,($the complement of L