Difference between revisions of "Contrary theorem"
From Encyclopedia of Mathematics
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A theorem obtained by replacing the condition and conclusion of a given initial theorem with their negations, and interchanging them. | A theorem obtained by replacing the condition and conclusion of a given initial theorem with their negations, and interchanging them. | ||
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| − | A contrary theorem is usually called a contrapositive theorem. Formally such a theorem is of the form: "If not B, then not A" , and is obtained by " | + | A contrary theorem is usually called a contrapositive theorem. Formally such a theorem is of the form: "If not B, then not A", and is obtained by "contraposition" (i.e. by interchanging the conclusion ($B$) and condition ($A$) and replacing each with its negation) from a given theorem: "If A, then B". |
Latest revision as of 18:01, 30 July 2014
A theorem obtained by replacing the condition and conclusion of a given initial theorem with their negations, and interchanging them.
Comments
A contrary theorem is usually called a contrapositive theorem. Formally such a theorem is of the form: "If not B, then not A", and is obtained by "contraposition" (i.e. by interchanging the conclusion ($B$) and condition ($A$) and replacing each with its negation) from a given theorem: "If A, then B".
How to Cite This Entry:
Contrary theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contrary_theorem&oldid=16561
Contrary theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contrary_theorem&oldid=16561