Q21,p3,j15. The transition function for the language L={w|na(w) and nb(w) are both odd} is given by.

Δ(q_0,a)=q_1.;              Δ(q_0,b)=q_2.

Δ(q_1,a)=q_0.               Δ(q_1,b)=q_3.

Δ(q_2,a)=q_3.               Δ(q_2,b)=q_0.

Δ(q_3,a)=q_2.               Δ(q_3,b)=q_1.

The initial and final states are.

Options.

A)     Q0 and q0

B)      Q0 and q1.

C)      Q0 and q2

D)     Q0 and q3.

Answer D.

Explanation.

Accepted words are { ab, ba, aaab,abaa, aaba,bbba-----}

A and b are of odd length. Hence from diagram from the above transitions. option D is correct.