- #1

Mathematicsresear

- 66

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## Homework Statement

a relation R⊆ℝ

^{2}

It is defined if and only if a

^{2}+b

^{2}=c

^{2}+d

^{2}where (a,b) ∧ (c,d)∈ℝ

^{2}

Find all equivalence classes

## Homework Equations

## The Attempt at a Solution

I said that the following set defines an equivalence class for the above problem:

[/B]

[(a,b)] = {(c,d)∈ℝ

^{2}: ((a,b),(c,d))∈R}⊆ℝ

^{2}

so I asked myself when is a

^{2}+b

^{2}=c

^{2}+d

^{2}such that (a,b) and (c,d) are elements of the relation and a subset of ℝ

^{2}.

I said when d= sqrt(a

^{2}+b

^{2}-c

^{2}) and a

^{2}+b

^{2}> c

^{2}

I am not sure what to do next.

I am not sure what to do next.