The answer to either / or questions is either yes or no.
This can lead to either laughter or a protest that question has not been answered.
If you end up with a protest, you can either ignore it or respond to it.
If you respond to the protest, you can either deny that you did not answer the question or reply that it is the answer to the question that results from the long chain of dichotomies engendered by the original query, namely, is this a legitimate quandary.
The answer is often No.