Etymology
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give (n.)
"capacity for yielding to pressure," 1868, from give (v.). The Middle English noun yeve, meant "that which is given or offered; a contribution of money," often as tribute, or in expectation of something in return.
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give (v.)

Old English giefan (West Saxon) "to give, bestow, deliver to another; allot, grant; commit, devote, entrust," class V strong verb (past tense geaf, past participle giefen), from Proto-Germanic *geban (source also of Old Frisian jeva, Middle Dutch gheven, Dutch geven, Old High German geban, German geben, Gothic giban), from PIE root *ghabh- "to give or receive." It became yiven in Middle English, but changed to guttural "g" by influence of Old Norse gefa "to give," Old Danish givæ.

Meaning "to yield to pressure" is from 1570s. Give in "yield" is from 1610s; give out is mid-14c. as "publish, announce;" meaning "run out, break down" is from 1520s. Give up "surrender, resign, quit" is mid-12c. To give (someone) a cold seems to reflect the old belief that one could be cured of disease by deliberately infecting others. What gives? "what is happening?" is attested from 1940. To not give a (some thing regarded as trivial and valueless) is from c. 1300 (early examples were a straw, a grass, a mite).

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up (n.)
"that which is up," 1530s, from up (adv.). Phrase on the up-(and-up) "honest, straightforward" first attested 1863, American English.
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up (adv.)

Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."

As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.

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up- 
prefix with various senses, from Old English up (adv.), corresponding to similar prefixes in other Germanic languages.
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give-away (n.)
also giveaway, "act of giving away," 1872, from verbal phrase give away, c. 1400 (of brides from 1719); see give (v.) + away (adv.). The phrase in the meaning "to betray, expose, reveal" is from 1878, originally U.S. slang. Hence also Related: give-away (n.) "inadvertent betrayal or revelation" (1882).
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up (v.)

1550s, "to drive and catch (swans)," from up (adv.). Intransitive meaning "get up, rise to one's feet" (as in up and leave) is recorded from 1640s. Sense of "to move upward" is recorded from 1737. Meaning "increase" (as in up the price of oil) is attested from 1915. Compare Old English verb uppian "to rise up, swell." Related: Upped; upping. Upping block, used for mounting or dismounting horses, carriages, etc., is attested from 1796 (earlier was horsing-block, 1660s).

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up (adj.)
c. 1300, "dwelling inland or upland," from up (adv.). Meaning "going up" is from 1784. From 1815 as "excited, exhilarated, happy," hence "enthusiastic, optimistic." Up-and-coming "promising" is from 1848. Musical up-tempo (adj.) is recorded from 1948.
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give-and-take (n.)
1769, originally in horse-racing, referring to races in which bigger horses were given more weight to carry, lighter ones less; from give (v.) + take (v.). General sense attested by 1778. Give and take had been paired in expressions involving mutual exchange from c. 1500. Give or take as an indication of approximation is from 1958.
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cover-up (n.)

also coverup, "means or act of concealing" some event or activity, 1922, from the verbal phrase (1872), from cover (v.) + up (adv.).

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