# 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 == | ||

+ | * [[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".