Definition: Contrapositive

A contrapositive of a conclusion \(x \Rightarrow y\) is a proposition, in which the antecedent \(x\), and the consequent \(y\) are inverted and negated, formally

\[\neg y\Rightarrow\neg x\] is the contrapositive of \[x\Rightarrow y.\]

We read the contrapositive \(\neg y\Rightarrow\neg x\) \["\text{if not }y,\text{ then not }x".\]

Lemmas: 1
Proofs: 2

Thank you to the contributors under CC BY-SA 4.0!