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Complementation of DFA works for all DFA is it true ?

Given DFA, a should be followed by a 'b',

In the complementation of this DFA the string aab is getting accepted 

a is getting followed by a 'b'

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at most one possibility does not occur , Like, when will be   ∀ false ? when we show a single counter example , right? and yes the complement of  "every a is followed by a b"  is true , when we show a single counter that that does not occur
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