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The phrase "a negative answer to" is correct and usable in written English.
It can be used when referring to a response that conveys disagreement, rejection, or denial regarding a question or proposal.
Example: "After reviewing the proposal, we received a negative answer to our request for funding."
Alternatives: "a negative response to" or "a refusal to".
Exact(49)
Many advocates of federal financing for embryo-destructive research begin from a negative answer to that question.
And, after a referendum last September delivered a negative answer to that question, what has driven so many Scots to abandon Labour for the separatist Scottish National Party (SNP)?
If he put off many people with his obsessional rants — his bourbonized public speeches in Irish brogue or Texas redneck — it was still hard for anyone of normal curiosity to give a negative answer to the question "Haven't I learned something about myself and my country from this man?" In January of this year, Mailer turned seventy-five.
This gives a negative answer to Oja's conjecture.
Some authors would give a negative answer to this question.
That result suggests a negative answer to Molyneux's question.
Similar(11)
His failure to give a consistently negative answer to question (2) lands him in flat contradiction with his official commitment to interpreting sacred texts in exactly the same way as profane texts (for, of course, as he indeed himself implies, in interpreting profane texts we may not assume that the texts are throughout true and therefore also self-consistent).
Hence, when answering the Chinese AAS, some may have given a (false) negative answer to physical abuse if no injury was caused by the abusive act.
The Verily project (Verily) crowdsources the task of verification by seeking rapid crowdsource evidence (in terms of an affirmative or negative answer) to answer verification questions.
A really satisfying theory of explanation should provide some principled answer to the question of whether all why explanation must be causal (and according to what notion of causal this is so or not so), rather than just assuming an affirmative (or negative) answer to this question.
When the women who had given a clearly positive or negative answer to the question concerning their interest in participating were compared, it was found that interested women had had more contacts with the health-care system – as measured by visits to a physician and a gynaecologist during the previous year – than had non-interested women.
More suggestions(15)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com