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I found this How do I verify that a DFA is equivalent to a NFA? but as it states it is not really a good question more of how can I check myself during an exam. Because as you might know to do this by hand for < 5 states is really hard to do without any mistake and I only get credit for a correct construction and not understanding that REGΣ = NEAΣ = DEAΣ

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Proving such a claim rigorously can be usually done with induction on word length $|w|$.

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