To acknowledge, confess, or admit guilt. Often used with to.(verb)
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Use "own up" in a sentence
"What? was I to leave it all, unclaimed and unregarded — in excess of morality and modesty — on the beach, to be honey-combed by white ants or to rot? or to honestly own up to that sentiment which is the most human of all?"
"Sarah had later learned that this was actually due to the anaesthetist having farted and been too embarrassed to own up at the time."