Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun A proposition derived by negating and permuting the terms of another, equivalent proposition; for example, All notY is notX is the contrapositive of All X is Y.
from The Century Dictionary.
 Of, pertaining to, or produced by contraposition: as, contrapositive propositions; contrapositive conversion.
 noun In logic, a contrapositive proposition.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun logic the
inverse of theconverse of a givenproposition
Etymologies
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Examples

I'm leaving out some steps here (which students always appropriately resent), but the above is all of a piece with something called the "contrapositive".

The '' 'contrapositive' '' of a statement of the form "A implies B" is the [[logic]] ally equivalent statement "notB implies notA."

The '' 'contrapositive' '' of a statement of the form "A implies B" is the [[logic]] ally equivalent statement "notB implies notA."

We can also see this in the contrapositive: having more than one sexual partner is by definition nonmonogamous.

A natural experiment that is the contrapositive to Korea would be Vietnam.
The Ratios, Bryan Caplan  EconLog  Library of Economics and Liberty

The contrapositive of this is that if you are not a U.S. national (e.g. you lose your nationality through the operation of the law) then it follows you are also not a citizen.
The Volokh Conspiracy » Peter Spiro on Lieberman’s CitizenshipStripping Legislation

But mythological creatures also performed a second, often contrapositive, argumentative function; commentators who rejected evolution regularly did so by dismissing these creatures.

If Messiahs are in the habit of denying themselves, surely the contrapositive is true.

The contrapositive of this is that if you are not a U.S. national e.g. you lose your nationality through the operation of the law then it follows you are also not a citizen.
The Volokh Conspiracy » Peter Spiro on Lieberman’s CitizenshipStripping Legislation

(If Messiahs are in the habit of denying themselves, surely the contrapositive is true.)
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