====== Contraposition ====== A [[logic:inferences:index|valid inference]] in which the [[glossary:antecedent|antecedent]] and [[glossary:consequent|consequent]] of a [[glossary:subjunction|subjunction]] are exchanged and both negated. As a formula, this looks as follows: > ''( A ⟶ B ) ≡ ( ⌐B ⟶ ⌐A )'' – “when A, then B” is logically equivalent to “when not-B, then not-A” For example: > “When it rains, the road gets wet” > is //logically equivalent// to > “When the road does not get wet, it does not rain”. ===== Description ===== The contraposition is a logical transformation rule that follows from the [[logic:inferences:modus_tollens|Modus Tollens]]. It is a [[glossary:commutativity|commutative]] operation, which means that the operation is valid in both directions. In the table below the valid transformations and a selection of invalid ones are compared: