have or havn't: Haven't you been to New York? - No, I haven't / No, I have

English as a Second Language English Vocabulary, Grammar and Idioms
1

as we know if the question is negative the answer is positive. so, why the third choise is best?
“Haven’t you been to New York?”
“_____ been there.”
Yes, I haven’t
Yes, I wasn’t
x No, I haven’t
No, I have

2

The answers with Yes and No can be either complete sentences : Yes, I am; Yes, I did; Yes, I have; or No, I am not; No, I did not; No, I have not.
or “abbreviated forms” : Yes. No.

3

sorry, I didn’t understand what are you meaning?