$($a$)$ Prove that if $D=(Q_D,,{}_D,\{q_o\},F_D)$ is the DFA constructed

from NFA $N=(Q_N,,{}_N,q_0,F_n)$ by the subset construction

then $L(D)=L(N).$

$($b$)$ Differentiate between $=(0,1)$ and ${}^1=(0,1).$

$($c$)$ Convert to a DFA the following NFA: