- #1

velouria131

- 13

- 0

Work:

Prove - if n is odd, prove that 3n+2 is even.

step 1 - if n is odd, n = 2k+1 for some integer k

step 2 - 3n + 2 = 3(2k+1) + 2 = 6k + 5

step 3 - This is my issue. A contrapositive proof for this problem would give not 'p', or, that 3n+2 is odd when n is odd. Do I now have to show that 6k + 5 is an odd number for any positive integer k? Or, should I just prove that 3n + 2 is odd when n is odd? If I take this route, could I choose another proof method, essentially having a 'proof within a proof'?