Question #142683
Statement: “The negative of any even integer is even.”
Using direct proof method
1
Expert's answer
2020-11-08T18:33:51-0500

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(k)−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).


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