Q $-$moves: Are they necessary?$).$ points$)$ Suppose $N=(Q,,,Q_0,F)$ is an NFA

with $-$moves.

$($a$)$ Build an NFA $N^{\text{'}}$ with no $-$moves that is equivalent to $N$ and has the same number of states

$($in fact, $N^{\text{'}}$ will be over the same set of states $-Q).$

Hint: Which states would be the starting states of $N^{\text{'}}?$ How would you modify the transition

function?

$($b$)$ Apply this transformation to the following example.