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Break down

Noun; a failure of a relationship or a system.

Give in

Noun; to finally agree to what someone wants, after refusing for a period of time.

Give up

Noun; declaring you're incurable or insoluble

What is the difference of Giving in and Giving up...?

Give up is used for quitting a habit or withdrawing from something. But give in is letting something happen or give way for something.