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Yeah thats really awkward and an odd thing to ask a candidate to do while you wait. I will be sure to avoid these people.

Out of curiosity what book is that DFA problem from?

That proof isn't a problem in the book; it's mentioned, with a hint for those inclined to derive it themselves, in the running text.

Thanks

Not sure what book the above poster used, but Sipser is an excellent book for learning about DFAs.