Contraposition
A valid inference in which the antecedent and consequent of a subjunction are exchanged and both negated.
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:
Contraposition (valid forms)  Invalid forms  

Origin  A → B (if A, then B  ⌐B → ⌐A (if not‑B, then not‑A)  A → B (if A, then B)  A → B (if A, then B) 

Transformation  ⌐B → ⌐A (if not‑B, then not‑A)  A → B (if A, then B  (if B, then A)  (if not‑A, then not‑B) 

See also:  Modus Tollens  Affirming the consequent  Denying the antecedent 
See also
More Information
 Contraposition on Wikipedia