give it up
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1. To yield something. This is a prime parking space—I'm not giving it up!
2. To abandon some task or goal. Oh, don't give up—you'll get this boiler fixed eventually.
3. To stop doing something in particular, often a habit. Lots of people have given up smoking, so I'm confident that you can too.
4. To surrender or yield. In this usage, a reflexive pronoun is used between "give" and "up." You need to give yourself up to the cops before an innocent person gets caught in the crossfire.
5. To doubt or remain skeptical of someone or something. I know I've failed a lot in the past year, but please, don't give up on me.
6. To fully pledge oneself to something. In this usage, a reflexive pronoun is used between "give" and "up." To deal with the grief, I gave myself up to my research.
7. To forsake someone or something. I gave the pizza up for lost when it didn't arrive in two hours.
give it upapplaud enthusiastically. informal
2004 New Zealand Listener Ladiiieees and gentlemen, give it up for Joseph Lin and the Auckland Philharmonia conducted by Steven Smith , coming to you live from the Auckland Town Hall.