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Math Help - set and relation

  1. #1
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    set and relation

    about the relation R={ (n,m)∈ NN: ∃r ∈ N: n^2 + m^2 = r^2}
    N is set of natural number.

    a)how to show the converse of R is equal to R?
    b)how to prove R is not the empty relation?
    c)how to prove R is not a function?
    Last edited by nyammo; March 22nd 2011 at 09:10 AM.
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  2. #2
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    Quote Originally Posted by nyammo View Post
    about the relation R={ (n,m)∈ NN: ∃r ∈ N: n^2 + m^2 = r^2}
    a)how to show the converse of R is equal to R?
    b)how to prove R is not the empty relation?
    c)how to prove R is not a function?
    a) You must mean inverse as in R=R^{-1}.
    Note that if m^2+n^2=r^2 then n^2+m^2=r^2.

    b) Is it true that (3,4)\in R~?

    c) Is every term of N the first term of some pair in R~?
    Last edited by Plato; March 22nd 2011 at 10:15 AM.
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