Contrapositive: Difference between revisions
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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 15:03, 8 May 2024
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".
