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

The proof of part ii. is the contrapositive of part i.

From Textbooks • Mar. 30, 2016

He has a wife and kids at home," says twin Nicole, who then states the contrapositive of the real lesson of reality programming: "Celebs like him are just average normal people.

From Time Magazine Archive

Prove indirectly the truth of the contrapositive of 'All A is B.' 4.

From Deductive Logic by Stock, St. George William Joseph

So a man may say, "All men are mortal," meaning that the angels never taste death, "angels" being the contrapositive of his subject "men".

From Logic, Inductive and Deductive by Minto, William

Under the same law, we know that he has a homogeneous contrapositive of the subject, a subject that admits of the same predicate, some other book in short.

From Logic, Inductive and Deductive by Minto, William