Answer to Question #142683 in Combinatorics | Number Theory for Christine Joy Sato

Question

Statement: “The negative of any even integer is even.”
Using direct proof method

Answer 1

Suppose n is any even integer. We must show that −n is even. By definition of even number, we have

n = 2k for some integer k. Multiply both sides by −1, we get

$−n = −(2k)= 2 \cdot(−k)$

Now let r = -k. Then r is an integer, r = −k= (−1) k. Hence, −n = 2r for some integer r.

And so by definition of even number, −n is even (it is divisible by 2).