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Meaning of non sequitur

non se•qui•tur

Pronunciation: (non sek'wi-tur, -toor" Lat. nōn se'kwi-toor"), [key]
  1. an inference or a conclusion that does not follow from the premises.
  2. a statement containing an illogical conclusion.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.