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Math Help - please help..

  1. #1
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    please help..

    Show that a relation R on a set X is symmetric if and only if whenever there is a directed edge from x to y in the digraph of R, there is a directed edge from y to x in the digraph of R.(i don't have the slightest idea how to do this...)
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  2. #2
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    Quote Originally Posted by kodirl
    Show that a relation R on a set X is symmetric if and only if whenever there is a directed edge from x to y in the digraph of R, there is a directed edge from y to x in the digraph of R.(i don't have the slightest idea how to do this...)
    A relation R on a set X is a set of some ordered pairs of X^2.
    Therefore, you can talk about G=(X,R) as a graph. But since R is symmetric on X you have that xy is in R (that means an edge in this digraph) means that yx is in E(G) too because of symetrry (that means an edge in this digraph).
    Last edited by ThePerfectHacker; August 9th 2006 at 11:23 AM.
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