(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X be Z*Z, i.e. X is the set of all ordered pairs of the form (x; y) with (x, y) are integers.

Define the relation R on X as follows:

(x1^2, x2^2)R(y1^2, y2^2) = (x1^2 + x2^2) = (y1^2 + y2^2)

2. Relevant equations

By definition, an equivalence relation bears the following characteristics,

reflexive,

transitive

symmetric

Further information here, http://www.math.csusb.edu/notes/rel/node3.html

3. The attempt at a solution

Not an equivalence relation?

Although it is reflective, the transitive and symmetric characteristics don't hold because if per say, we have x1 = 1, x2 = 2, y1 = 3, y2 = 4, the relation doesn't hold to start with...

Is this a strong explanation? Or better suggestions?

I feel that it's more complicated than this?

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# Homework Help: Equivalence Relation

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