Below is what I have so far. I'm pretty sure that it is transitive, but I'm not sure how to prove that it is. Prove that A is or isn't transitive.

Below is what I have so far. I'm pretty sure that it is transitive, but I'm not sure how to prove that it is. Prove that A is or isn't transitive.

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Suppose $x-y$ is rational and $y-z$ is rational, then its sum its rational, but this is $$x-y + y -z = x-z$$