contrapositive

contra- +‎ positive

contrapositive (plural contrapositives)

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

• 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.

• converse
• inverse