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The phrase "and do not admit" is correct and usable in written English.
It can be used in contexts where you want to instruct someone not to acknowledge or accept something.
Example: "In this discussion, please focus on the facts and do not admit any personal biases."
Alternatives: "and refrain from acknowledging" or "and avoid accepting".
Idiom
Do's and don't's.
The do's and don't's are what is acceptable or allowed or not within an area or issue, etc.
Exact(2)
"The city and its contractors have an array of powerful defenses to these claims and do not admit any liability," the chief lawyer for the city, James E. Tyrrell Jr., said in a statement on Friday.
Pferschy and Schauer [33] prove that the maximum flow problems with both negative and positive disjunctive constraints are NP-hard and do not admit a Polynomial-Time Approximation Scheme (PTAS).
Similar(58)
Some men go to them and don't admit it, but more and more men are comfortable admitting it".
Many people think AIDS is a bad disease, so they don't talk about it and don't admit they have it".
They're the ones who drink and don't admit it.
We have a choice to behave correctly and honorably or not and if we don't, and don't admit it then we are in denial.
Keep the one page profile of your boss at home and don't admit it exists.
The company blamed a rogue engineer, and did not admit any wrongdoing in the matter.
Both companies settled the cases out of court and did not admit wrongdoing.
Ogilvy agreed in 2002 to pay $1.8 million to settle a related civil accusation and did not admit wrongdoing.
Few of these artists had any special allegiance to Atlantic, however, and most had musical styles that had been established elsewhere and did not admit of modification.
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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