Decide whether a DFA accepts the empty language

Let $X = \{\langle M \rangle\ |\ M\text{ is a finite state machine and }L(M) = \emptyset\}$ where $\langle M \rangle$ is an encoding of the
machine $M$. Is $X$ Turing decidable? Why or why not?

Re-read your textbook chapter on DFAs and NFAs -- you'll find everything you need to know there.

See also the following questions, which both have answers to your question embedded in their answers (make sure to read carefully):

• Can a Turing machine decide the language $L_\emptyset$ of machines with empty language?

• Undecidable among these for turing machine

Next time, tell us what you have tried, to solve the exercise on your own.

StackExchange Computer Science Q#18616, answer score: 4