intro to formal language by peter linz

Question

Is it true that for every nfa M = (Q, Σ,δ,q0,F)the complement of L (M)is equal to the set {w ∈ Σ* :
δ*; (q0,w) ∈ (Q – F) = Ø}? If so, prove it; if not, give a counterexample.

plz explain this ques by taking some simple example

Answer 1

It seems true what you mentioned in the question. The complement of a language accepted by an FA will be, subtract all strings accepted by that FA from Sigma*.

Lc = {w ∈ Σ* :δ*; (q0,w) ∈ (Q – F) = Ø} it means we are considering all those strings from Sigma* which will not be accepted by this NFA, and this only is the definition of complement of a machine.

PS: I think in quesiton it should be Q INTERSECTION F = Phi