Exercise 1.2.8 (Same parity)

Question

Two integers are said to be of same {\bf parity} if they are both even or both odd; if one is even and the other odd, they are said to be of opposite parity, or of different parity. Given any two integers, prove that their sum and their difference are of the same parity.

Richard Ganaye · Accepted Answer

\begin{proof} If $m$ and $n$ are integers, $(m+n) - (m-n) = 2n$ is even, therefore $m+n$ and $m-n$ are of same parity.

(If $m-n$ is odd, then $m+n = (m-n) + 2n$ is odd, and if $m-n$ is even, then $m+n = (m-n) + 2n$ is even.)
\end{proof}

Exercise 1.2.8 (Same parity)

Answers

Comments

Exercise 1.2.8 (Same parity)

Answers

Comments

Add answer