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Contraposition

A valid inference in which the antecedent and consequent of a subjunction are exchanged and both negated.

Note: This should not be confused with a contradiction.

As a formula this looks as follows:

( A → B ) ⇔ ( ⌐B → ⌐A )

For example:

When it rains, the road gets wet.
⇒ If the road does not get wet, it does not rain.

Description

The contraposition is a logical transformation rule that follows from the Modus Tollens. It is valid in both directions, which means that the two forms A → B as well as ⌐B → ⌐A are equivalent.

In the table below the valid transformations and a selection of invalid ones are compared:

See also

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