Problem $9[$Do not use Jflap for this problem. $]$

Find a simple regular expression for each of the following languages. Do not use Jflap. The justification of your answer is a very important part of your grade.

a$.$ L$1=\{$ w in $\{$a$,$b$\}*$:$$ na$($w$)>=2$ and nb$($w$)>=1\}.$ Justify your answer.

Note: The a$$s and b$$s can be in any order. Your regular expression should handle this.

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b$.$ L$2=\{$ w in $\{0,1\}*$:$$ w is the binary representation of a prime number between $2$ and $15.\}$Justify your answer.

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c$.$ L$3=\{$ anbm: n $>3,0<=$ m $<=3\}$Justify your answer.