Yonkers Resident tax - Moved to Yonkers in November, did not pay it

I'm filing my 2019 taxes and I'm at the residency questions.

I lived in a different city for most of the year and only moved to Yonkers in mid-November of 2019. I didn't have a job and I don't pay rent where I live, so I said that I'm not reporting the Yonkers resident tax in my NYS return. My permanent address was in Yonkers by December 31st, 2019, but then I was asked to explain why I didn't report it in my return.

My question is- should I change my address to what it was for most of the year (in the different city, not Yonkers) and just not mention Yonkers, or should I keep what I have?

I'm not sure how saying that I didn't pay the tax is going to affect my return or what the explanation should be. Taking Yonkers out altogether seems easier to explain.

Thanks!

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