contrapositive

English

Etymology

From contra- +‎ positive.

Noun

contrapositive (plural contrapositives)

1. (logic) The logical equivalent of a given logical implication.

Usage notes

• From a conditional statement, its contrapositive is defined as follows:

  Proposition: "If P then Q."

  Contrapositive: "If not Q then not P."

• While the inverse and converse of a true conditional statement are not necessarily true, the contrapositive always is. 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.
• Proposition: "If we have good weather, then the Yankees play tomorrow."

  Contrapositive: "If the Yankees don't play tomorrow, then we don't have good weather."

• Proposition: "If you submit every homework assignment, then you pass this course."

  Contrapositive: "If you don't pass this course, then you don't submit every homework assignment."

• Proposition: "If you have sleep apnea, then you snore in your sleep."

  Contrapositive: "If you don't snore in your sleep, then you don't have sleep apnea."

Derived terms

• contrapositively

Translations

the inverse of the converse of a given proposition

• Finnish: kontrapositio
• German: Kontraposition f
• Icelandic: mótskilyrðing f
• Japanese: 対偶 (ja) (taigū)
• Polish: kontrapozycja f
• Spanish: contraposición (es) f

See also

• converse
• inverse