I came a across a question where there were some statements made on Finite Automata, DFA and their states.
One such statements in the question was that a "Every DFA accepting a finite language must contain a dead state"
And the answer stated the statement to be true, and showed some DFA where there was a dead state following the accepting/final state.
Yes, dead states after the final state is possible but what about languages like $(a+b)^*$ ? It is a finite language and there is no need for a dead state in it's DFA:
There is no dead state in this DFA. Am I making a mistake somewhere?