contrapositive

English

Etymology

contra- +‎ positive

Noun

contrapositive (plural contrapositives)

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

Usage notes

• From a conditional statement, its inverse, its converse, and its contrapositive are defined 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 conditional statement 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.
• In Classical logic (more generally, logics employing the law of excluded middle), a conditional statement is true if and only if its contrapositive is true. In this framework, if the statement "If I can't speak Latin, then I'm not Roman" is true, then the statement "If I'm Roman, then I can speak latin" must also be true

Translations

the inverse of the converse of a given proposition

• Finnish: kontrapositio
• German: Kontraposition f
• Icelandic: mótskilyrðing f

See also

• converse
• inverse