$($a$)$ Convert the above NFA in to an equivalent DFA.

$($b$)$ Convert the regular expression $a(ab)**(b{)}^{**},$ over the alphabet $=\{a,b\},$ to an equivalent NFA.

$($c$)$ Convert the regular expression $ab**a(ab)**ba(ab)**,$ over the alphabet $=\{a,b\},$ to an equivalent NFA.

$($d$)$ Let $=\{a,b\}.$ Let $A$