$2$ DFAs and Regular Expressions

Let $M$ be the DFA given by:

set of states $Q=\{q_0,q_1,q_2\}$

initial state $q_0$

set of final states $F=\{q_0,q_2\}$

transition function $$ given by

a$)$ Draw a state$/$transition diagram for the automaton $M.$

$(1$pt$)$

b$)$ Construct a regular expression $e$ such that $L(M)=L(e).$

$(2$pt$)$