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contra- +‎ positive


contrapositive (plural contrapositives)

  1. (logic) The inverse of the converse of a given proposition.

Usage notes[edit]

  • From a proposition, its inverse, its converse, and its contrapositive are derived as follows:
    Proposition: "If P then Q."
    Inverse: "If not P then not Q."
    Converse: "If Q then P."
    Contrapositive: "If not Q then not P."
  • If a proposition is true then its contrapositive is, too. Thus, if the statement "If I'm Roman, then I can speak Latin" is true, then it logically follows that the statement "If I can't speak Latin, then I'm not Roman" must also be true.


See also[edit]