How would I go about doing this?
I assume proving it's reflexive, symmetrical and transitive
Show that the relation $R = \{(x, y):3x − 5y \text{ is even }\}$ is an equivalence relationship.
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CiaPan
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Are there any confines on $x$ and $y$? For example, what if $x=0.1$ and $y=0.2$. Is $1.3$ even? If you want $x$ and $y$ to be integers then I recommend you used $m$ and $n$ instead of $x$ and $y$. – Fly by Night Mar 12 '16 at 23:03
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There are no confines. Why would I use $m$ and $n$? – Mar 12 '16 at 23:08
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There are confines: you're assuming that $x$ and $y$ are integers. It's common to use $m$ and $n$ for integers. – Fly by Night Mar 13 '16 at 12:58
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Assuming $R \subset {\mathbb Z}^2$.
$3x-5y$ is even iff $3x$ and $5y$ are both even or both odd.
Terms are even iff respective variables are even, so the given relation is equivalent to 'both variables are even or both are odd'.
The three basic properties are obvious now.
CiaPan
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