To welsh is defined as to go back on your word or fail to honor a promise.(verb)
When you promise to pay your son's college tuition if he gets into Harvard and then he gets in and you tell him you don't have the money after all, this is an example of a time when you welsh on your promise.
The definition of Welsh is something related to Wales, a principality of Great Britain that is located west of central England.(adjective)
If a food is characteristic of Wales, this is an example of a food that would be described as Welsh.
See welsh in Webster's New World College Dictionary
Origin: 19th-c. slang, prob. < Welsh, with reference to alleged character traits of the Welsh
Origin: ME Wel(i)sch < OE Welisc < Wealh, Briton, foreigner < PGmc *walh-, Celt < Celt name > L Volcae, name of a Celtic people of S France
See welsh in American Heritage Dictionary 4
intransitive verb welshed also welched, welsh·ing also welch·ing, welsh·es also welch·es
Origin: Origin unknown.
Origin: Middle English Walische
Origin: , from Old English Wǽlisc
Origin: , from Wealh, foreigner, Welshman, Celt
Origin: , perhaps of Celtic origin.
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