# Difference between revisions of "Contrapositive"

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A [[conditional]] statement is usually expressed as | A [[conditional]] statement is usually expressed as | ||

− | If '''P''', then '''Q''' | + | If '''P''', then '''Q'''. |

The contrapositive statement is usually expressed as | The contrapositive statement is usually expressed as | ||

− | If not '''Q''', then not '''P''' | + | If not '''Q''', then not '''P'''. |

where '''P''' denotes a condition and '''Q''' denotes another condition. | where '''P''' denotes a condition and '''Q''' denotes another condition. | ||

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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". | ||

+ | |||

+ | == See also == | ||

+ | * [[Logic]] |

## Latest revision as of 13:08, 19 December 2016

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".