In specific how can I setup a contradiction proof if $3n+2$ is odd then $n$ is odd? I don't want the answer. I just want to know how to set up the proof by contradiction.
I think that I should assume if $3n+2$ is not odd, then $n$ is even then prove that $n$ is in fact odd.
I am unsure of what to assume and what do I prove. I am trying to teach a class you can do the same proof in many different ways.
I know how to prove with a direct proof. Assume $3n+2=2k+1$ and prove $n=2J+1$
I know how to prove with a contrapositive proof. Assume $n=2J$ and prove $3n+2=2k$
How would I do the same setup for a contradiction proof?