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I need help with question as following:

  1. $X= \mathbb{Z}\times \mathbb{Z}$ I need to define the relation $R$ on $X$ as follows:

    $(X_1,X_2)R(Y_1,Y_2) \longleftrightarrow (X_1)^2+(X_2)^2=(Y_1)^2+(Y_2)^2$

Can you prove it using (X)R(Y) ?

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Since you are new, I want to give you some advice about the site: To get the best possible answers, you should explain what your thoughts on the problem are so far. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people are much more willing to help you if you show that you've tried the problem yourself. If this is homework, please add the [homework] tag; people will still help, so don't worry. – Zev Chonoles Feb 2 '13 at 18:21
Is X = $\mathbb{Z}\setminus\{0\} \times \mathbb{Z}\setminus\{0\}$? That is, $\mathbb{Z}\setminus \{0\}$ is the set of integers not including zero? – amWhy Feb 2 '13 at 18:22
@akerman I edited your question using $\LaTeX$. Please check if everything is in order and let us know. – Git Gud Feb 2 '13 at 18:23
its exactly as it is written and I'm so confused with those two questions and not sure how to solve them – akerman Feb 2 '13 at 18:29
This looks all too familiar to the homework I have set. I will make sure that I will bring this up to the Director of Studies should I find out who are you. – monsmanr Feb 3 '13 at 21:21

1 Answer 1

Hint: For describing the equivalence class, think about using cross-multiplication to determine if two fractions are equal.

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protected by Nate Eldredge Feb 3 '13 at 23:17

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