Peter Linz Edition 4 Exercise 2.3 Question 6 (Page No. 62)

Question

Is it true that for every nfa $M = (Q,Σ,δ,q_0,F)$ the complement of $L(M)$ is equal to the set

{$w ∈ Σ^*: δ^*(q_0,w) $ $\cap$ $(Q-F)$ $\neq$ $Ø$}? If so, prove it. If not, give a counterexample.