# contrapositive

con·tra·pos·i·tiveLogic a proposition obtained by negating and transposing the terms of a given proposition: the

*contrapositive*of “All A is B” is “All not-B is not-A”## contrapositive

noun

*Logic*

A proposition derived by negating and permuting the terms of another, equivalent proposition; for example,

*All not-Y is not-X*is the contrapositive of*All X is Y.*## contrapositive

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.