contrapositive

English

Etymology

contra- +‎ positive

Noun

contrapositive (plural contrapositives)

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

Usage notes

• 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.

Translations

the inverse of the converse of a given proposition

• Finnish: kontrapositio
• (deprecated template usage) {{trans-mid}}
• Icelandic: mótskilyrðing f

See also

• converse
• inverse