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Math Help - equivalence relations

  1. #1
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    equivalence relations

    I need help with the following question:

    Define a relation R on natural numbers by aRb whenever ab is a square. show R is an equivalence relation.
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  2. #2
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    Quote Originally Posted by baker11108 View Post
    I need help with the following question:

    Define a relation R on natural numbers by aRb whenever ab is a square. show R is an equivalence relation.

    Where're you stuck? Reflexivity and symmetry are immediate, and transitivity requires a tiny trick: ac=\frac{(ab)(bc)}{b^2} ...

    Tonio
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  3. #3
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    I am having trouble even before that. We are unsure if we are reading the question right or not. We are not real familiar with equivalence relations. Let's say a=8 and b=2. Then ab=16 which is a square. So aRb by reflexivity because they are elements of natural numbers or what?
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  4. #4
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    Quote Originally Posted by baker11108 View Post
    I am having trouble even before that. We are unsure if we are reading the question right or not. We are not real familiar with equivalence relations. Let's say a=8 and b=2. Then ab=16 which is a square. So aRb by reflexivity because they are elements of natural numbers or what?

    You need to re-read your definitions carefully: 8R2 because 8\cdot 2 is a square (in the natural numbers, of course)...what has this to do with reflexivity??

    Tonio
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