$(20$ Points$)$ Given the following language,$=\{\},$

$($a$)(5$ Points$)(4$ Points$)$ List $2$ strings are in and $(1$ Point$)1$ strings are not

in $.$

$[$ANSWER$]$

$($b$)(15$ Points$)$ Construct a Turing Machine $($TM$)$ for recognizing $.$

$[$ANSWER$]$