$($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: $6.($a$)$ Convert the following regular expression to NFA with $$ transition:

I. $,1^{**}0(0+1{)}^{**}10$

II$.,(a|b{)}^{**}$abb

$($b$)$ Prove that, every language defined by a regular expression is also defined by a

finite automaton$\mathrm{.}4.($a$)$ Define transition table and transition diagram with example.

$4$

$($b$)$ Let us use hat$()$ to describe the processing of input $00101$ by the NFA of following

$6$

figure. please answer all those separately and also add q name before ans