Etymology
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Words related to distrust

dis- 
Origin and meaning of dis-

word-forming element of Latin origin meaning 1. "lack of, not" (as in dishonest); 2. "opposite of, do the opposite of" (as in disallow); 3. "apart, away" (as in discard), from Old French des- or directly from Latin dis- "apart, asunder, in a different direction, between," figuratively "not, un-," also "exceedingly, utterly." Assimilated as dif- before -f- and to di- before most voiced consonants.

The Latin prefix is from PIE *dis- "apart, asunder" (source also of Old English te-, Old Saxon ti-, Old High German ze-, German zer-). The PIE root is a secondary form of *dwis- and thus is related to Latin bis "twice" (originally *dvis) and to duo, on notion of "two ways, in twain" (hence "apart, asunder").

In classical Latin, dis- paralleled de- and had much the same meaning, but in Late Latin dis- came to be the favored form and this passed into Old French as des-, the form used for compound words formed in Old French, where it increasingly had a privative sense ("not"). In English, many of these words eventually were altered back to dis-, while in French many have been altered back to de-. The usual confusion prevails.

As a living prefix in English, it reverses or negatives what it is affixed to. Sometimes, as in Italian, it is reduced to s- (as in spend, splay, sport, sdain for disdain, and the surnames Spencer and Spence).

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trust (n.)
c. 1200, "reliance on the veracity, integrity, or other virtues of someone or something; religious faith," from Old Norse traust "help, confidence, protection, support," from Proto-Germanic abstract noun *traustam (source also of Old Frisian trast, Dutch troost "comfort, consolation," Old High German trost "trust, fidelity," German Trost "comfort, consolation," Gothic trausti "agreement, alliance"), from Proto-Germanic *treuwaz, source of Old English treowian "to believe, trust," and treowe "faithful, trusty," from PIE root *deru- "be firm, solid, steadfast."

from c. 1300 as "reliability, trustworthiness; trustiness, fidelity, faithfulness;" from late 14c. as "confident expectation" and "that on which one relies." From early 15c. in legal sense of "confidence placed in a one who holds or enjoys the use of property entrusted to him by its legal owner;" mid-15c. as "condition of being legally entrusted." Meaning "businesses organized to reduce competition" is recorded from 1877. Trust-buster is recorded from 1903.
trust (v.)
c. 1200, from Old Norse treysta "to trust, rely on, make strong and safe," from traust (see trust (n.)). Related: Trusted; trusting.
distrustful (adj.)

"full of distrust, suspicious, mistrustful," 1590s, from distrust (n.) + -ful. Related: Distrustfully; distrustfulness (1570s).