give a damn
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give a damn (about somebody/something)(slang)
to be interested or involved He sent his son to parochial school because he believes that those schools give a damn.
Usage notes: also used with verbs like could and might to mean someone is not concerned about something: A significant portion of kids in class could give a damn.
not give a damn(informal)
to not be interested in or worried about something or someone He can think what he likes. I don't give a damn. (often + about ) Most companies don't give a damn about the environment. (often + question word) I've made my decision and I don't give a damn what they think.