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Homework Help: Proof Equivalence relation

  1. Feb 15, 2010 #1
    In R x R , ley (x,y) R (u,v) if ax^2 +by^2=au^2 + bv^2, where a,b >0. Determine the relation R is an equivalnce relation. Prove or give a counter example
     
  2. jcsd
  3. Feb 16, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi nikie1o2! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    Tell us how far you've got, and where you're stuck, and then we'll know how to help! :smile:
     
  4. Feb 16, 2010 #3
    Re: Welcome to PF!

    Hello, thank you for the warm welcome.

    I have done equivalence relations before but with just two variables not 4. So i was confused on how to prove the reflexive, symmetric & transitive properties.

    For reflexive i was thinking if (x,y)R(x,y) then ax^2+by^2=ax^2+by^2- so that is true
    Symmetry: (x,y)R(u,v) then (u,v)R(x,y) is true

    For Transitive i knoe if(x,y)R(u,v) and (u,v)R(a,b), then (x,y)R(a,b). Im just confused on how to show the equations for that and that it's true...
     
  5. Feb 16, 2010 #4

    Redbelly98

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    Moderator's note:
    Homework assignments or textbook style exercises for which you are seeking assistance are to be posted in the appropriate forum in our https://www.physicsforums.com/forumdisplay.php?f=152" area. This should be done whether the problem is part of one's assigned coursework or just independent study.
     
    Last edited by a moderator: Apr 24, 2017
  6. Feb 17, 2010 #5

    tiny-tim

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    Hello nikie1o2! :smile:

    (Please use the X2 tag just above the Reply box :wink:)
    Just write out the definitions of (x,y)R(u,v) and (u,v)R(a,b) … then it should be obvious! :smile:

    (btw, the equivalence classes are a well-known geometrical shape … can you se which?)
     
  7. Feb 17, 2010 #6

    Redbelly98

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    Just a comment: using "a" and "b" is a bad choice of variable names in this problem. May I suggest using "s" and "t" instead? I.e., use
    (u,v)R(s,t)​
    instead of
    (u,v)R(a,b)​
    when working out the transitive property.
     
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