I know similar questions about how to answer negative questions were asked before. But still I am confused.
If somebody asked you "You do not want to play with me?", I thought it's correct to answer "Yes, we do want to play with you", or "No, we do not want to play with you." But then I read this sentence in my daughter's picture book "Elephant and Piggy" (the author is American), they answered "No. We do want to play with you." So I asked one of my American friends, who told me it's correct. My friend said if the question was asked as "Don't you want to play with me?", you have to answer in another way, like "Yes, we do want to play with you" and "No, we do not want to play with you".
From Can I Play Too? by Mo Willems
Best Answer
Conversational English often makes use of a negative that negativizes an entire implied negative utterance, and is not just a Yes or No answer in response to the verb. This is a kind of double negative at utterance level, and is perfectly grammatical and used for effect.
Question: "You do not want to play with me?"
Answer: No! [It is not that I do not want to play with you.=implied negative utterance] The answer continues on the next line: We do want to play with you.
If the Answer in the kid's book had been: "Yes", it would mean: Yes, that's right. I do not want to play with you.
The question being asked is not a simple yes-no binary one:
The word no refers to an implied utterance. There is no other possible interpretation here and in conversation, these implied sentences utterances are very common.
Question: "You do not want to go to the movies me?"
The yes or no to this question refutes or accepts the entire implication.
And I am sure that someone here can write this out in better logical or philosophical notation with brackets:
VERSUS
And the amazing part is that very young children get it until they are browbeaten by adults. There is logic at play here, not just grammar. :)