Q$1.$ Consider the following languages on $$:$=\{p,q\}$ and show the design of DFA and regular expression to

recognize $L_1,L_2$ and $L_3.$

a$)L_l$:$=\{\begin{array}{c}in{}^{*}|\end{array}$ initiates with $pp$ however does not finish with $\{$:$pp\}.$

b$)L_2$:$=\{\begin{array}{c}in{}^{*}|\end{array}$ finishes with $qq$ however does not start with $\{$:$qq\}.$

c$)L_3$:$=\{\begin{array}{c}in{}^{*}|\end{array}$ initiates with $pq$ however does not finish with $\{$:$pq\}.$