turing machine

Question

( 

1.   All strings of even length over {a,b}
2.   Complement of (a+b)*
3.   (a+b)*
4.   All strings of odd length over {a,b}

Comments

there is no way to reach q_2. Then how we can reach q_f ?

Answer should be B. complement of (a+b)* is empty language.

---

Can u please show it with the state diagram

---

You don't really need a state Diagram to figure that out...
You see, there is no movement of R/W head from State q1 to q2 whatsoever), but in the question, they took q2 as it is and passed BLANK to final state qf , hence! obviously, there's no a' and b's to be seen in the machine's o/p whatsoever.

Look below, Ashwin has already posted the state diag.

Answer 1

there is no way to reach q_2. Then no way to reach q_{f .} Hence nothing is accepted by this TM

Answer should be B. complement of (a+b)* is empty language.