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Math Help - Equivalence Relation question

  1. #1
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    Equivalence Relation question

    Let A = NxN, and define a relation R on A by (a,b)R(c,d) iff ab = cd.

    I already proved that this is a relation.
    But the question also asks to find the equivalence class E(9,2), and find an equivalence class with exactly 2 elements, one with 3 elements and one with 4 elements.
    Im not sure how to do that with this question, or what that last part even means.

    any help?
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  2. #2
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    Quote Originally Posted by p00ndawg View Post
    Let A = NxN, and define a relation R on A by (a,b)R(c,d) iff ab = cd.
    But the question also asks to find the equivalence class E(9,2), and find an equivalence class with exactly 2 elements, one with 3 elements and one with 4 elements.
    E(9,2)=\{(9,2),(2,9),(1,18),(18,1),(3,6),(6,3)\}

    E(1,2)=\{(1,2),(2,1)\}

    Now you finish.
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  3. #3
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    just to make sure im understanding,

    E(1, 4)= {3 elements} ??
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  4. #4
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    Quote Originally Posted by p00ndawg View Post
    just to make sure im understanding,

    E(1, 4)= {3 elements} ??
    What are the elements?
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  5. #5
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    Quote Originally Posted by plato View Post
    what are the elements?

    (1,4), (4,1) (2,2)?
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  6. #6
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    Quote Originally Posted by p00ndawg View Post
    (1,4), (4,1) (2,2)?
    Exactly.
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