Logic 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
con·tra·pos·i·tiveWebster's New World College Dictionary, Fifth Edition Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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"contrapositive." YourDictionary, n.d. Web. 14 January 2019. <https://www.yourdictionary.com/contrapositive>.
APA Style
contrapositive. (n.d.). Retrieved January 14th, 2019, from https://www.yourdictionary.com/contrapositive
contrapositive
noun
LogicA 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.
THE AMERICAN HERITAGE® DICTIONARY OF THE ENGLISH LANGUAGE, FIFTH EDITION by the Editors of the American Heritage Dictionaries. Copyright © 2016, 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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MLA Style
"contrapositive." YourDictionary, n.d. Web. 14 January 2019. <https://www.yourdictionary.com/contrapositive>.
APA Style
contrapositive. (n.d.). Retrieved January 14th, 2019, from https://www.yourdictionary.com/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.
English Wiktionary. Available under CC-BY-SA license.
Link to this page
Cite this page
MLA Style
"contrapositive." YourDictionary, n.d. Web. 14 January 2019. <https://www.yourdictionary.com/contrapositive>.
APA Style
contrapositive. (n.d.). Retrieved January 14th, 2019, from https://www.yourdictionary.com/contrapositive
