Relation $R$ on $V$ is given by $x+y$ is even

Question

A relation $R$ on $V$ is given by $x+y$ is even. How can we show that if integers $x$ and $y$ are $R$-related then either $x$ and $y$ are both even or $x$ and $y$ are both odd? I've been looking through Google for information on how to answer relation questions but without any luck at all. I think I need to use equivalence relations but I am not entirely sure.

You have removed the question from your question! It's incomprehensible now. — TonyK, Mar 11 '14 at 18:22
Regarding the title, it's equivalent to $x,y$ having the same parity (odd/even). — AlexR, Mar 11 '14 at 19:45

score 3 · Accepted Answer · answered Mar 10 '14 at 16:10

If $x$ is even and $y$ is odd, then $x=2k$ for some integer $k$ and $y=2l+1$ for some integer $l$, so $x+3y=2k+3(2l+1)=2(k+3l+1)+1$ is odd.

If $x$ is odd and $y$ is even, then $x=2m+1$ for some integer $m$ and $y=2n$ for some integer $n$, so $x+3y=2m+1+3(2n)=2(m+3n)+1$ is odd.

Relation $R$ on $V$ is given by $x+y$ is even

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