give up
give up {v.}
1a. To stop trying to keep; surrender; yield.
The dog had the ball in his mouth and wouldn't give it up.
Jimmy is giving up his job as a newsboy when he goes back to school.
Contrast: HOLD ON TO.
1b. To allow; permit.
Ford gave up two walks in the first inning.
2. To stop doing or having; abandon; quit.
The doctor told Mr. Harris to give up smoking.
Jane hated to give up her friends when she moved away.
3. To stop hoping for, waiting for, or trying to do.
Johnny was given up by the doctors after the accident, but he lived just the same.
When Mary didn't come by nine o'clock, we gave her up.
I couldn't do the puzzle so I gave it up.
4. To stop trying; quit; surrender.
The war will be over when one of the countries gives up.
The other team gave up after we scored three touchdowns.
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Source: A Dictionary of American Idioms