Let n be an integer. Prove that if n + 5 is odd, then 3n + 2 is even. So the instructions say to use a direct proof. I couldnt figure that method out, so I used a controposition proof and that seemed to work ok. Here are my contraposition steps: Assume 3n+2 is odd Def of odd: n=2k+1 n+5=2k+1+5 = 2k+6 = 2(k+3) n+5 is even (multiple of 2) since negation of conclusion implies hypothesis is false, original statement is true. Im pretty sure thats correct, but how could this be done using a direct proof?