How do I prove that if $2\nmid n$ then $2|(n+1)$? I'd like to prove a very simple fact, but it's stumping me: namely, that if $2 \nmid n$ then $2\mid(n+1)$.
How would this usually be done?

If 2 does not divide $n$ then $n$ is must be odd thus $n+1$ must be even thus by definition of even 2 must divide $n+1$
