Etymology
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delinquency (n.)

"failure or omission of duty or obligation," 1630s, from Late Latin delinquentia "fault, crime, delinquency," from Latin delinquentem (see delinquent).

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debauched (adj.)

"seduced or corrupted from duty or virtue, vitiated in morals or purity of character," 1590s, past-participle adjective from debauch (v.). Related: Debauchedness.

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skive (v.2)
"evade duty," usually with off, 1919, probably from earlier sense "move lightly and quickly, dart" (1854), of unknown origin. Related: Skived; skiving.
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task (n.)
early 14c., "a quantity of labor imposed as a duty," from Old North French tasque (12c., Old French tasche, Modern French tâche) "duty, tax," from Vulgar Latin *tasca "a duty, assessment," metathesis of Medieval Latin taxa, a back-formation of Latin taxare "to evaluate, estimate, assess" (see tax (v.)). General sense of "any piece of work that has to be done" is first recorded 1590s. Phrase take one to task (1680s) preserves the sense that is closer to tax.

German tasche "pocket" is from the same Vulgar Latin source (via Old High German tasca), with presumable sense evolution from "amount of work imposed by some authority," to "payment for that work," to "wages," to "pocket into which money is put," to "any pocket."
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delinquent (n.)

late 15c., "one who fails to perform a duty or discharge an obligation," also, generally, "an offender against the law," a noun use from Latin delinquentum (nominative delinquens), present participle of delinquere "to fail; be wanting, fall short; do wrong, transgress, offend," from de- "completely" (see de-) + linquere "to leave" (from PIE root *leikw- "to leave"). As an adjective, "failing or neglectful in duty," from c. 1600 in English.

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official (adj.)

late 14c., "performing a service" (a sense now obsolete); c. 1400, "required by duty," from Old French oficial "official; main, principal" (14c., Modern French officiel) and directly from Late Latin officialis "of or belonging to duty, service, or office," from Latin officium "service, kindness, favor; official duty, function, business; ceremonial observance," literally "work-doing," from ops (genitive opis) "power, might, abundance, means" (related to opus "work," from PIE root *op- "to work, produce in abundance") + combining form of facere "to make, to do" (from PIE root *dhe- "to set, put").

Meaning "pertaining to an office or official position" is from c. 1600. That of "derived from the proper office or officer," hence "authorized," is by 1854.

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brig (n.)
"two-masted square-rigged vessel," 1720, colloquial shortening of brigantine (q.v.). Meaning "a ship's jail" is by 1841, American English, perhaps from the use of such vessels as prison ships upon retirement from active duty.
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duly (adv.)

"rightly, properly; adequately, sufficiently; in accordance with duty or moral obligation," late 14c., duweliche, from dewe "due" (see due) + -liche (see -ly (2)).

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imposition (n.)
late 14c., "a tax, duty, tribute," from Old French imposicion "tax, duty; a fixing" (early 14c.), from Latin impositionem (nominative impositio) "a laying on," noun of action from past participle stem of imponere "to place upon," from assimilated form of in "into, in" (from PIE root *en "in") + ponere "to put, place" (past participle positus; see position (n.)). Sense of "the act of putting (something) on (something else)" is from 1590s. Meaning "an act or instance of imposing" (on someone) first recorded 1630s, a noun of action from impose, which is unrelated to the earlier word.
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dereliction (n.)

1590s, "abandonment, state of being forsaken or abandoned" (formerly with a wider range than in modern use, such as of the sea withdrawing from the land), from Latin derelictionem (nominative derelictio) "an abandoning; a disregarding, neglecting," noun of action from past-participle stem of derelinquere (see derelict).

Sense of "act of leaving with an intention not to reclaim or reuse" is from 1610s. Meaning "failure, unfaithfulness, neglect" (with regard to duty, etc.) is by 1778. Phrase dereliction of duty attested from 1776.

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