Prove by contraposition that if n is an integer and 3n 2 is

Prove by contraposition that if n is an integer and 3n + 2 is even then n is even.

Solution

Proof by contraposition:

Prove the statement by showing the contrapositive. Suppose n is odd and show that 3n + 2 is odd.

n = 2k +1 for some integer k with the definition of odd integers.

3n +2 = 3(2k+1) + 2

= 6k +5

= 6k +4 +1

=2(3k+2) + 1, so 3n+2 be 2 times an integer + 1, so it is odd.