You know what it looks like… but what is it called?
TAKE THE QUIZ“not give”
The following 3 entries include the term not give.
not give a monkey's
idiom: to not care at all about something.
not give a toss
idiom: to not care at all about something
not give (someone) the time of day
idiom: to not give (someone) any attention or help
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Merriam-Webster unabridged