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Math Help - equivalence relations!

  1. #1
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    equivalence relations!

    Hey everyone, I have some basic equivalence relation problems here that I've been trying to work on for the past while, and even though I understand the concept behind them, I'm still struggling with getting the right answers, I think. I dont expect you to answer them all, but it would be great if you could get me started!

    For each of the following equivalence relations on R, find [0] and [3]

    (1) Let R be the relation given by aRb iff |a|=|b| for all a,bR
    (2) Let S be the relation given by aSb iff sin a = sin b for all a,bR
    (3) Let T be the relation given by aTb iff there is some nZ such that a=2^n b, for all a,bN

    [The answers I got for (1) are [0]={0} and [3]={-3,3}... is this correct? Thanks!]
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  2. #2
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    Quote Originally Posted by mrsplant View Post
    Hey everyone, I have some basic equivalence relation problems here that I've been trying to work on for the past while, and even though I understand the concept behind them, I'm still struggling with getting the right answers, I think. I dont expect you to answer them all, but it would be great if you could get me started!

    For each of the following equivalence relations on R, find [0] and [3]

    (1) Let R be the relation given by aRb iff |a|=|b| for all a,bR
    (2) Let S be the relation given by aSb iff sin a = sin b for all a,bR
    (3) Let T be the relation given by aTb iff there is some nZ such that a=2^n b, for all a,bN

    [The answers I got for (1) are [0]={0} and [3]={-3,3}... is this correct? Thanks!]
    Your answers for the first one are correct. What about the rest?
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  3. #3
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    i'm not sure... am I supposed to set sin a = sin b = 0 and sin a = sin b = 3 respectively for the second one?
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  4. #4
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    Quote Originally Posted by mrsplant View Post
    i'm not sure... am I supposed to set sin a = sin b = 0 and sin a = sin b = 3 respectively for the second one?
    \left( {\forall n \in \mathbb{Z}} \right)\left[ {\sin (n\pi ) = 0} \right]\,\& \,\sin (x) = \sin (x + 2n\pi )
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