contrapositive
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English
Etymology
Noun
contrapositive (plural contrapositives)
- (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
Derived terms
Translations
the inverse of the converse of a given proposition
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