Difference between revisions of "Contrapositive"

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Given the conditional statement "If a polygon has 3 sides, then it is a triangle", the contrapositive is "If a polygon is not a triangle, then it does not have 3 sides".
 
Given the conditional statement "If a polygon has 3 sides, then it is a triangle", the contrapositive is "If a polygon is not a triangle, then it does not have 3 sides".
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== See also ==
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* [[Logic]]

Revision as of 22:09, 29 July 2006

A contrapositive of a statement is always true, assuming that the conditional statement is true. However, if the conditional statement is false, then the contrapositive is also false.

A conditional statement is usually expressed as

If P, then Q.

The contrapositive statement is usually expressed as

If not Q, then not P.

where P denotes a condition and Q denotes another condition.

Examples

Given the conditional statement "If a polygon has 3 sides, then it is a triangle", the contrapositive is "If a polygon is not a triangle, then it does not have 3 sides".

See also

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