Definition
to cease ownership, use, or claim to something
He decided to give up all rights to the property belonging to his parents.
Faced with severe financial difficulties, she was forced to give up her vacation plans.
As he aged, he began to give up his pursuit of a professional career.
to abandon hope that a specific event will occur
After numerous failures, I have given up hope that he will change.
As time passed, we began to give up hope of winning the match.
She gave up hope of ever achieving success in this field.