Etymology
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untruth (n.)

Old English untreowþ "unfaithfulness, treachery," from un- (1) "not" + truth (n.). Similar formation in Old Norse utrygð. Meaning "falsehood" is attested from mid-15c., as is that of "a lie." Related: Untruthful.

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inveracity (n.)

"lack of truthfulness; an untruth," 1789, from in- (1) "not, opposite of" + veracity.

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lying (adj.2)

"untruthful," early 13c., present-participle adjective from lie (v.1) "to tell an untruth." Related: Lyingly.

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lying (n.2)

"untruthfulness, falsehood," c. 1300, "the telling of lies," verbal noun from lie (v.1) "to tell an untruth."

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lie (n.1)

"an untruth; conscious and intentional falsehood, false statement made with intent to deceive," Middle English lie, from Old English lyge, lige "lie, falsehood," from Proto-Germanic *lugiz (source also of Old Norse lygi, Danish løgn, Old Frisian leyne (fem.), Dutch leugen (fem.), Old High German lugi, German Lüge, Gothic liugn "a lie"), from the root of lie (v.1).

To give the lie to "accuse directly of lying" is attested from 1590s. Lie-detector is recorded by 1909.

In mod. use, the word is normally a violent expression of moral reprobation, which in polite conversation tends to be avoided, the synonyms falsehood and untruth being often substituted as relatively euphemistic. [OED]
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mendacious (adj.)

"given to lying, speaking falsely; having the characteristics of a lie, false, untrue," 1610s, from French mendacieux and directly from Latin mendacium "a lie, untruth, falsehood, fiction," from mendax (genitive mendacis) "lying, deceitful," from menda "fault, defect, carelessness in writing," from PIE root *mend- "physical defect, fault" (see amend (v.)). The sense evolution of Latin mendax was influenced by mentiri "to speak falsely, lie, deceive." Related: Mendaciously; mendaciousness.

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lie (v.1)

"speak falsely, tell an untruth for the purpose of misleading," Middle English lien, from Old English legan, ligan, earlier leogan "deceive, belie, betray" (class II strong verb; past tense leag, past participle logen), from Proto-Germanic *leuganan (source also of Old Norse ljuga, Danish lyve, Old Frisian liaga, Old Saxon and Old High German liogan, German lügen, Gothic liugan), a word of uncertain etymology, with possible cognates in Old Church Slavonic lugati, Russian luigatĭ; not found in Latin, Greek, or Sanskrit. Emphatic lie through (one's) teeth is from 1940s.

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pseudo- 

often before vowels pseud-, word-forming element meaning "false; feigned; erroneous; in appearance only; resembling," from Greek pseudo-, combining form of pseudēs "false, lying; falsely; deceived," or pseudos "falsehood, untruth, a lie," both from pseudein "to tell a lie; be wrong, break (an oath)," also, in Attic, "to deceive, cheat, be false," but often regardless of intention, a word of uncertain origin. Words in Slavic and Armenian have been compared; by some scholars the Greek word is connected with *psu- "wind" (= "nonsense, idle talk"); Beekes suggests Pre-Greek origin.

Productive in compound formation in ancient Greek (such as pseudodidaskalos "false teacher," pseudokyon "a sham cynic," pseudologia "a false speech," pseudoparthenos "pretended virgin"), it began to be used with native words in later Middle English with a sense of "false, hypocritical" (pseudoclerk "deceitful clerk;" pseudocrist "false apostle;" pseudoprest "heretical priest;" pseudoprophete; pseudofrere) and has been productive since then; the list of words in it in the OED print edition runs to 13 pages. In science, indicating something deceptive in appearance or function.

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un- (1)

prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").

The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.

It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.

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