Question

Consider three integers m, n, and p. Put the steps in the correct order to prove that m + p is even if m + n and n + p are even integers.

Answer 1

Hi,

Explanation:

`\boxed{m,n,p\in\mathbb{N}:m+n \in 2\mathbb{N}\ and\ n+p \in 2\mathbb{N}\Longrightarrow\ m+p \in 2\mathbb{N}}\\\\\\m+n \in 2\mathbb{N} \Longrightarrow\ m+n=2*a, a \in \mathbb{N}\\n+p \in 2\mathbb{N} \Longrightarrow\ n+p=2*b, b \in \mathbb{N}\\\Longrightarrow\ m+p=2a+2b-2n=2(a+b+n)\\\Longrightarrow\ m+p \in2 \mathbb{N}`