Show the NFA that results from applying the construction of Figure $2\mathrm{.}7$

$2\mathrm{.}4($a$)$

$($b$)$ Apply the transformation illustrated by Example $2\mathrm{.}14$ to create an

to the regular expression letter $($ letter $|$ digit $)*.$ equivalent DFA.

$($c$)$ Apply the transformation illustrated by Example $2\mathrm{.}15$ to minimize the DFA.