contrapositive

American  

[kon-truh-poz-i-tiv] / ˌkɒn trəˈpɒz ɪ tɪv /

adjective

1. of or relating to contraposition.

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noun

1. a contrapositive statement of a proposition.

contrapositive British  

/ ˌkɒntrəˈpɒzɪtɪv /

adjective

1. placed opposite or against

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noun

1. logic

   1. a conditional statement derived from another by negating and interchanging antecedent and consequent

   2. a categorial proposition obtained from another, esp validly, by any of a number of operations including negation, transferring the terms, changing their quality, and also possibly weakening from universal to particular

Etymology

Origin of contrapositive

First recorded in 1855–60; contraposit(ion) + -ive

Explanation

In logic, a contrapositive is a new version of a statement like "If the sun rises there, then that's east" that reverses and negates it, but is still logically sound: "If that's not east, then the sun doesn't rise there." Contrapositive is derived from the Latin contraponere, "to place opposite." To form a contrapositive, you take a conditional statement, also called an "If…then" statement, flip around the hypothesis and conclusion, and make both negative. If the original statement is true, the contrapositive will be true, too. For example, if you start with the sentence "If a shape has three sides, it's a triangle," its contrapositive, "If a shape isn't a triangle, it does not have three sides," is also valid.

Example Sentences

There is no reason why the propositional form should not be called the Converse by Contraposition, or the Contrapositive Converse, in accordance with traditional usage.

From Logic, Inductive and Deductive by Minto, William

The best known secondary form of Immediate Inference is the Contrapositive, and this is the converse of the obverse of a given proposition.

From Logic Deductive and Inductive by Read, Carveth

Footnote 6: It is to be regretted that a practice has recently crept in of calling this form, for shortness, the Contrapositive simply.

From Logic, Inductive and Deductive by Minto, William

But no Converse or Contrapositive of such a Disjunctive can be obtained, except by first casting it into the hypothetical or categorical form.

From Logic Deductive and Inductive by Read, Carveth

This Converse is obtained by substituting for the predicate term its Contrapositive or Contradictory, not-P, making the consequent change of Quality, and simply converting.

From Logic, Inductive and Deductive by Minto, William