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Math Help - Reflexive And Symmetric

  1. #16
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    Re: Reflexive And Symmetric

    Quote Originally Posted by Hartlw View Post
    The possible relations on {1.2.3} are:
    {(1,1), (2,2), (3,3)}
    {(1,2), (2,3), (1,3)}
    {(2,1) (3,2), (3,1)}
    {(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)}
    {(1,1), (2,2), (3,3), (2,1), (3,2), (3,1)}
    You missed a whole lot of the relations on \{1,2,3\}.
    There are 2^9=512 possible relations.
    Any subset of \{1,2,3\}\times\{1,2,3\}.
    As I said you don't know what a relation is.
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  2. #17
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    Re: Reflexive And Symmetric

    Quote Originally Posted by Plato View Post
    You missed a whole lot of the relations on \{1,2,3\}.
    There are 2^9=512 possible relations.
    Any subset of \{1,2,3\}\times\{1,2,3\}.
    As I said you don't know what a relation is.
    Not if 1,2,3 are integers, or you accept meaningless definitions which are really not relations. Frankly, I wavered on acceptable subsets. I don't believe they apply for the integers, depending on the definition of "relation," for example {(1,1), (1,2)}, but that's a topic for another discussion. In any event, your post 2 set is not a possible relation for the integers.
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  3. #18
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    Re: Reflexive And Symmetric

    Quote Originally Posted by Hartlw View Post
    Not if 1,2,3 are integers, or you accept meaningless definitions which are really not relations. Frankly, I wavered on acceptable subsets. I don't believe they apply for the integers, depending on the definition of "relation," for example {(1,1), (1,2)}, but that's a topic for another discussion. In any event, your post 2 set is not a possible relation for the integers.
    If \mathcal{R}=\{(1,1),~(2,2),~(3,3),~(1,2),~(2,1)\} \subseteq (\mathbb{Z}\times\mathbb{Z}) then it is a relation in the integers.
    Last edited by Plato; November 7th 2012 at 02:02 PM.
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