# Equivalence Relations and Equivalence Classes

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I don't know how to show the following are equivalence relations and if they are, how to describe equivalence classes.

1. a^2 + b^2=c^2 + d^2 where a,b,c,d are real numbers(describe equivalence cl)

2. For a pair of fractions a/b and c/d define a/b ~ c/d if ab=cd(same here)

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##### Solution Summary

Equivalence Relations and Equivalence Classes are investigated.

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1. (a,b)~(c,d) if a^2+b^2=c^2+d^2. ~ is an equivalent relation. We check the following.

(1) (a,b)~(a,b), obviously

(2) (a,b)~(c,d) ...

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