Old English andswaru "a response, a reply to a question," from and- "against" (from PIE root *ant- "front, forehead," with derivatives meaning "in front of, before") + -swaru "affirmation," from swerian "to swear" (see swear), suggesting an original sense of "sworn statement rebutting a charge." Meaning "solution of a problem" is from c. 1300.
It is remarkable that the Latin expression for answer is formed in exactly the same way from a verb spondere, signifying to engage for, to assure. [Hensleigh Wedgwood, "A Dictionary of English Etymology," 1859]
A common Germanic compound (cognates: Old Saxon antswor, Old Norse andsvar, Old Frisian ondser, Danish and Swedish ansvar), implying a Proto-Germanic *andswara-. The simpler idea of "a word in reply" is expressed in Gothic anda-vaurd, German Antwort.
word-forming element meaning "lacking, cannot be, does not," from Old English -leas, from leas "free (from), devoid (of), false, feigned," from Proto-Germanic *lausaz (cognates: Dutch -loos, German -los "-less," Old Norse lauss "loose, free, vacant, dissolute," Middle Dutch los, German los "loose, free," Gothic laus "empty, vain"), from PIE root *leu- "to loosen, divide, cut apart." Related to loose and lease.