A type of [[Proof]] to prove $p\to q$ that assumes $\neg q$ with steps to prove $\neg p$. >[!example] If $n^2$ is an even integer, then $n$ is an even integer. > >[[Proof by Contraposition]]: > >Assume: $\neg q$, n is an odd integer. > >Then: $\exists k \in \Z$ such that $n=2k+1$ . > >So $n^2=(2k+1)^2$ >$ >\begin{align} >n^2&= (2k+1)^2 \\ > &= 4k^2 +4k + 1\\ > &= 2(2k^2+2k)+1 \end{align} $ >Because $2k^2+2k$ is an [[Integer]], this proves $\neg p$ to be true.