Could you explain each steps?

3. (a) Give the set up and construction steps of a proof that shows that the class of regular languages over an alphabet & is closed under the operation EvenLengthStringsOnly(L), defined as EvenLengthStringsOnly(L) = {W E L such that [w] is even}. Solution: Let L be a regular language, then there is some DFA M = (Q, 2,8,90, F) that recognizes L. Create a new DFA M = (Q', 2,8', q0', F') as follows: Q' = Q {EVEN, ODD} for allr EQ, XE for all rEQ, 8'((r, EV EN),x) = (8(r, ), ODD) 8'((r,ODD), x) = (8(r, x), EVEN) q0' = (q0, EVEN) F' = {(r, EVEN) | reF} 3. (a) Give the set up and construction steps of a proof that shows that the class of regular languages over an alphabet & is closed under the operation EvenLengthStringsOnly(L), defined as EvenLengthStringsOnly(L) = {W E L such that [w] is even}. Solution: Let L be a regular language, then there is some DFA M = (Q, 2,8,90, F) that recognizes L. Create a new DFA M = (Q', 2,8', q0', F') as follows: Q' = Q {EVEN, ODD} for allr EQ, XE for all rEQ, 8'((r, EV EN),x) = (8(r, ), ODD) 8'((r,ODD), x) = (8(r, x), EVEN) q0' = (q0, EVEN) F' = {(r, EVEN) | reF}