give up vs forgo

give up and forgo both are verbs.

Word	Noun	Adjective	Verb	Adverb
give up	No	No	Yes	No
forgo	No	No	Yes	No

As verbs, forgo is a hypernym of give up; that is, forgo is a word with a broader meaning than give up:

Other hypernyms of give up include dispense with, forego, foreswear, relinquish, waive.

As verbs, give up and forgo are synonyms defined as:

give up and forgo: lose (something) or lose the right to (something) by some error, offense, or crime

Other synonyms of give up include forego, forfeit, throw overboard, waive.

give up (verb)	forgo (verb)
stop maintaining or insisting on; of ideas or claims	lose (something) or lose the right to (something) by some error, offense, or crime
give up in the face of defeat of lacking hope; admit defeat	do without or cease to hold or adhere to
give up or agree to forgo to the power or possession of another	be earlier in time; go back further
stop consuming
give up with the intent of never claiming again
relinquish possession or control over
lose (something) or lose the right to (something) by some error, offense, or crime
part with a possession or right
give up what is not strictly needed
allow the other (baseball) team to score
leave (a job, post, or position) voluntarily
put an end to a state or an activity