Etymology
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falsity (n.)

c. 1300, "deceitfulness, treachery, dishonesty," from Old French fauseté "falsehood" (12c., Modern French fausseté), from Late Latin falsitatem (nominative falsitas), from Latin falsus "erroneous, mistaken" (see false). From late 14c. as "untrue statement or doctrine;" from 1570s as "character of being not true."

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vanity (n.)

c. 1200, "that which is vain, futile, or worthless," from Old French vanite "self-conceit; futility; lack of resolve" (12c.), from Latin vanitatem (nominative vanitas) "emptiness, aimlessness; falsity," figuratively "vainglory, foolish pride," from vanus "empty, void," figuratively "idle, fruitless," from PIE *wano-, suffixed form of root *eue- "to leave, abandon, give out." Meaning "self-conceited" in English is attested from mid-14c. Vanity table is attested from 1936. Vanity Fair is from "Pilgrim's Progress" (1678).

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