Answer to Question #256968 in Discrete Mathematics for htd

Question

Show by giving a proof by contrapositive, that if 3n+2 is odd, then n is odd

Answer 1

The contrapositive of the above statement is as follows.

If n isn't odd then 3n+2 isn't odd (If n is even then 3n+2 is even).

Let us prove the obtained statement:

If n is even then $n = 2k,\,k \in Z$ . Then

$3n + 2 = 3 \cdot 2k + 2 = 6k + 2$

6k is even, 2 is even, so 6k+2 is even (as the sum of two even numbers).

Q. E. D.