Meaning of “give sb up” in the English Dictionary

"give sb up" in British English

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give sb up

phrasal verb with give uk /ɡɪv/ us /ɡɪv/ verb gave, given
give sb up for dead also give up on sb

to think that someone is certain to die or to be dead:

The doctors had virtually given her up for dead, but she eventually recovered.
After a three-day search on the mountain, they gave him up for dead.

(Definition of “give sb up” from the Cambridge Advanced Learner’s Dictionary & Thesaurus © Cambridge University Press)