Etymology
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Words related to whether

*kwo- 
also *kwi-, Proto-Indo-European root, stem of relative and interrogative pronouns.

It forms all or part of: cheese (n.2) "a big thing;" cue (n.1) "stage direction;" either; hidalgo; how; kickshaw; neither; neuter; qua; quality; quandary; quantity; quasar; quasi; quasi-; query; quib; quibble; quiddity; quidnunc; quip; quodlibet; quondam; quorum; quote; quotidian; quotient; ubi; ubiquity; what; when; whence; where; whether; which; whither; who; whoever; whom; whose; why.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kah "who, which;" Avestan ko, Hittite kuish "who;" Latin quis/quid "in what respect, to what extent; how, why," qua "where, which way," qui/quae/quod "who, which;" Lithuanian kas "who;" Old Church Slavonic kuto, Russian kto "who;" Old Irish ce, Welsh pwy "who;" Old English hwa, hwæt, hwær, etc.
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either 

Old English ægðer, contraction of æghwæðer (pron., adv., conj.) "each of two, both," from a "always" (see aye (adv.)) + ge- collective prefix + hwæðer "which of two, whether" (see whether). Cognate with Old Frisian eider, Dutch ieder, Old High German eogiwedar, German jeder "either, each, every").

Modern sense of "one or the other of two" is late 13c. Adverbially, for emphasis, "in any case, at all," especially when expressing negation, by 1828. Use of either-or to suggest an unavoidable choice between alternatives (1931) in some cases reflects Danish enten-eller, title of an 1843 book by Kierkegaard.

neither (conj., adv.)

"not one or the other," Middle English neither, naither, nether, from Old English nawþer, contraction of nahwæþer, literally "not of two," from na "no" (from PIE root *ne- "not") + hwæþer "which of two" (see whether). Spelling altered c. 1200 by association with either. Paired with nor from c. 1300; earlier with ne. Meaning "not in any case, in no case, not at all" is from 1550s. Also used in late Old English as a pronoun. As an adjective, "not either," mid-14c.

neuter (adj.)

late 14c., neutre, in grammar, of nouns, pronouns, etc., "neither masculine nor feminine in gender," also of verbs, "having middle or reflexive meaning, neither active nor passive," from Latin neuter "of the neuter gender," literally "neither one nor the other," from ne- "not, no" (from PIE root *ne- "not") + uter "either (of two)" (see whether). The Latin word is probably a loan-translation of Greek oudeteros "neither, neuter." From 1520s it also had the sense of "taking neither side" which now generally goes with neutral (adj.).

As a noun from mid-15c., "the neuter gender;" by 1797 of certain animals (among bees, ants, etc.) that are of neither sex and incapable of generation.