fray (v.)youdaoicibaDictYouDict
"wear off by rubbing," c. 1400, from Old French fraiier, froiier "to rub against, scrape; thrust against" (also in reference to copulation), from Latin fricare "to rub, rub down" (see friction). Intransitive sense "to ravel out" (of fabric, etc.) is from 1721. The noun meaning "a frayed place in a garment" is from 1620s. Related: Frayed; fraying.
swear (v.)youdaoicibaDictYouDict
Old English swerian "take an oath" (class VI strong verb; past tense swor, past participle sworen), from Proto-Germanic *swarjan-, (cognates: Old Saxon swerian, Old Frisian swera, Old Norse sverja, Danish sverge, Middle Dutch swaren, Old High German swerien, German schwören, Gothic swaren "to swear"), from PIE root *swer- (1) "to speak, talk, say" (cognates: Old Church Slavonic svara "quarrel," Oscan sverrunei "to the speaker").

Also related to the second element in answer. The secondary sense of "use bad language" (early 15c.) developed from the notion of "invoke sacred names." Swear off "desist as with a vow" is from 1898. Swear in "install in office by administration of an oath" is from 1700 in modern use, echoing Old English.
wear (v.)youdaoicibaDictYouDict
Old English werian "to clothe, put on, cover up," from Proto-Germanic *wazjan (cognates: Old Norse verja, Old High German werian, Gothic gawasjan "to clothe"), from PIE *wos-eyo-, from root *wes- (4) "to clothe" (cognates: Sanskrit vaste "he puts on," vasanam "garment;" Avestan vah-; Greek esthes "clothing," hennymi "to clothe," eima "garment;" Latin vestire "to clothe;" Welsh gwisgo, Breton gwiska; Old English wæstling "sheet, blanket;" Hittite washshush "garments," washanzi "they dress").

The Germanic forms "were homonyms of the vb. for 'prevent, ward off, protect' (Goth. warjan, O.E. werian, etc.), and this was prob. a factor in their early displacement in most of the Gmc. languages" [Buck]. Shifted from a weak verb (past tense and past participle wered) to a strong one (past tense wore, past participle worn) in 14c. on analogy of rhyming strong verbs such as bear and tear. Secondary sense of "use up, gradually damage" (late 13c.) is from effect of continued use on clothes. To wear down (transitive) "overcome by steady force" is from 1843. To wear off "diminish by attrition or use" is from 1690s.