Consider the Turing Machine $($TM$)T($over the input alphabet $=\{a,b\})$ given below.

Hint: Trace the execution of the TM on a few strings of a and $b$ s so that you can see how

it works.

$($a$)$ What is the shortest word that would be accepted by $T?$

$($b$)$ What is accept$(T)?$

$($c$)$ What is reject $(T)?$

$($d$)$ What is loop $(T)?$