Dic: give up on

• He urged them not to give up on peace efforts.
• My teachers gave up on me.

PHRASAL VERB | If you give up on something or someone, you decide that you will never succeed in doing what you want to with them, and you stop trying to.

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Cf.

PHRASAL VERB | If you give up, you decide that you cannot do something and stop trying to do it.

• After a fruitless morning sitting at his desk he had given up.

.... Cobuild