Explore BrainMass

Explore BrainMass

    Equivalence Relations and Equivalence Classes

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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)

    © BrainMass Inc. brainmass.com December 15, 2022, 5:38 pm ad1c9bdddf

    Solution Preview

    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) ...

    Solution Summary

    Equivalence Relations and Equivalence Classes are investigated.