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Math Help - Help with Relations equivalence Q

  1. #1
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    Help with Relations equivalence Q

    Hi I would be grateful for replies on how to do this Q.

    Define a relation R on R^2 (reals squared) by

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

    Prove that R is an equivalence relation. Describe geometrically the equivalence classes.

    Thanks
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  2. #2
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    Re: Help with Relations equivalence Q

    Quote Originally Posted by James7361539 View Post
    Hi I would be grateful for replies on how to do this Q.

    Define a relation R on R^2 (reals squared) by

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

    Prove that R is an equivalence relation. Describe geometrically the equivalence classes.

    Thanks
    you need to show

    reflexivity, i.e. aRa

    symmetry, i.e. aRb <--> bRa

    transitivity, i.e. (aRb,bRc) --> aRc

    I don't see that restricting your points to Q makes any difference.

    given that your relation is just the square of the distance between the points (x1,y1) and (x2,y2) the geometric interpretation of the equivalence classes should be pretty clear.
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  3. #3
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    Re: Help with Relations equivalence Q

    Quote Originally Posted by romsek View Post
    I don't see that restricting your points to Q makes any difference.
    I think that the OP is using Q for the word "question" and not $\mathbb{Q}$.
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  4. #4
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    Re: Help with Relations equivalence Q

    Quote Originally Posted by Plato View Post
    I think that the OP is using Q for the word "question" and not $\mathbb{Q}$.
    yes quite. That will teach me to start this before finishing my coffee.
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