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Math Help - Total relation

  1. #1
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    Total relation

    How can I proof that if L is a universal relation that R total relation\equiv L = L \circ R. It is pretty obvious that it is true, but how do I prove it?
    Last edited by gordo151091; April 2nd 2011 at 12:13 PM.
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  2. #2
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    Could you explain what Rtotalrelation is? Also, is universal relation the one that contains all possible pairs? Finally, by L\cdot R do you mean the composition L\circ R?
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  3. #3
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    Quote Originally Posted by emakarov View Post
    Could you explain what Rtotalrelation is? Also, is universal relation the one that contains all possible pairs? Finally, by L\cdot R do you mean the composition L\circ R?
    R total relation is

    \exists z|: xRz))" alt="R \equiv (\forall x |\exists z|: xRz))" />

    Yes, the universal relation is the one that contains all pairs

    Yes, I did mean the composition. Edited the OP.
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  4. #4
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    This is just a matter of using the notation.
    If (a,b) is any pair then \left( {\exists c} \right)\left[ {(c,b) \in R} \right] because R is total.
    Because L is universal (a,c)\in L so (a,b)\in L\circ R.
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  5. #5
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    Quote Originally Posted by Plato View Post
    If (a,b) is any pair then \left( {\exists c} \right)\left[ {(c,b) \in R} \right] because R is total.
    Because L is universal (a,c)\in L so (a,b)\in L\circ R.
    I think it should say that for any (a,b) there exists a c such that (a,c)\in R because R is total. Then (c,b)\in L because L is universal, so (a,b)\in L\circ R.
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  6. #6
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    Thanks, that is correct. It was either to early or the cut and paste.
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