Question about Anti Symmetricity












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$begingroup$


If there are no relations on the set R where (a,b) ∈ R and (b,a) ∈ R is it anti symmetrical because you can't evaluate if a = b or is it not anti-symmetrical because you can't evaluate if a = b?



ex)

R = {(1,1),(2,1),(2,2),(3,1),(3,3),(4,1),(4,2),(4,3),(4,4)}

I don't see a relation where (a,b) and (b,a) ∈ R so I can't evaluate if a = b






discrete-mathematics







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    0












    $begingroup$


    If there are no relations on the set R where (a,b) ∈ R and (b,a) ∈ R is it anti symmetrical because you can't evaluate if a = b or is it not anti-symmetrical because you can't evaluate if a = b?



    ex)

    R = {(1,1),(2,1),(2,2),(3,1),(3,3),(4,1),(4,2),(4,3),(4,4)}

    I don't see a relation where (a,b) and (b,a) ∈ R so I can't evaluate if a = b






    discrete-mathematics







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      If there are no relations on the set R where (a,b) ∈ R and (b,a) ∈ R is it anti symmetrical because you can't evaluate if a = b or is it not anti-symmetrical because you can't evaluate if a = b?



      ex)

      R = {(1,1),(2,1),(2,2),(3,1),(3,3),(4,1),(4,2),(4,3),(4,4)}

      I don't see a relation where (a,b) and (b,a) ∈ R so I can't evaluate if a = b






      discrete-mathematics







      share|cite|improve this question









      $endgroup$




      If there are no relations on the set R where (a,b) ∈ R and (b,a) ∈ R is it anti symmetrical because you can't evaluate if a = b or is it not anti-symmetrical because you can't evaluate if a = b?



      ex)

      R = {(1,1),(2,1),(2,2),(3,1),(3,3),(4,1),(4,2),(4,3),(4,4)}

      I don't see a relation where (a,b) and (b,a) ∈ R so I can't evaluate if a = b






      discrete-mathematics




      discrete-mathematics






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      asked Oct 24 '14 at 4:43









      John DoeJohn Doe

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          $begingroup$

          This relation is antisymmetric. If there is no $a,b in R$ such that $aneq b$ and where both $(a,b) in R$ and $(b,a) in R$, then $R$ is antisymmetric.



          For this particular relation, the only four times we have both $(a,b) in R$ and $(b,a) in R$ are where $a=b$, namely:



          begin{eqnarray*}
          a=1, ; b=1 && qquad text{since $(1,1) in R$} \
          a=2, ; b=2 && qquad text{since $(2,2) in R$} \
          a=3, ; b=3 && qquad text{since $(3,3) in R$} \
          a=4, ; b=4 && qquad text{since $(4,4) in R$}. \
          end{eqnarray*}






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            $begingroup$

            This relation is antisymmetric. If there is no $a,b in R$ such that $aneq b$ and where both $(a,b) in R$ and $(b,a) in R$, then $R$ is antisymmetric.



            For this particular relation, the only four times we have both $(a,b) in R$ and $(b,a) in R$ are where $a=b$, namely:



            begin{eqnarray*}
            a=1, ; b=1 && qquad text{since $(1,1) in R$} \
            a=2, ; b=2 && qquad text{since $(2,2) in R$} \
            a=3, ; b=3 && qquad text{since $(3,3) in R$} \
            a=4, ; b=4 && qquad text{since $(4,4) in R$}. \
            end{eqnarray*}






            share|cite|improve this answer











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              1












              $begingroup$

              This relation is antisymmetric. If there is no $a,b in R$ such that $aneq b$ and where both $(a,b) in R$ and $(b,a) in R$, then $R$ is antisymmetric.



              For this particular relation, the only four times we have both $(a,b) in R$ and $(b,a) in R$ are where $a=b$, namely:



              begin{eqnarray*}
              a=1, ; b=1 && qquad text{since $(1,1) in R$} \
              a=2, ; b=2 && qquad text{since $(2,2) in R$} \
              a=3, ; b=3 && qquad text{since $(3,3) in R$} \
              a=4, ; b=4 && qquad text{since $(4,4) in R$}. \
              end{eqnarray*}






              share|cite|improve this answer











              $endgroup$
















                1












                1








                1





                $begingroup$

                This relation is antisymmetric. If there is no $a,b in R$ such that $aneq b$ and where both $(a,b) in R$ and $(b,a) in R$, then $R$ is antisymmetric.



                For this particular relation, the only four times we have both $(a,b) in R$ and $(b,a) in R$ are where $a=b$, namely:



                begin{eqnarray*}
                a=1, ; b=1 && qquad text{since $(1,1) in R$} \
                a=2, ; b=2 && qquad text{since $(2,2) in R$} \
                a=3, ; b=3 && qquad text{since $(3,3) in R$} \
                a=4, ; b=4 && qquad text{since $(4,4) in R$}. \
                end{eqnarray*}






                share|cite|improve this answer











                $endgroup$



                This relation is antisymmetric. If there is no $a,b in R$ such that $aneq b$ and where both $(a,b) in R$ and $(b,a) in R$, then $R$ is antisymmetric.



                For this particular relation, the only four times we have both $(a,b) in R$ and $(b,a) in R$ are where $a=b$, namely:



                begin{eqnarray*}
                a=1, ; b=1 && qquad text{since $(1,1) in R$} \
                a=2, ; b=2 && qquad text{since $(2,2) in R$} \
                a=3, ; b=3 && qquad text{since $(3,3) in R$} \
                a=4, ; b=4 && qquad text{since $(4,4) in R$}. \
                end{eqnarray*}







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Oct 28 '14 at 8:49

























                answered Oct 27 '14 at 14:51









                Mick AMick A

                8,8252825




                8,8252825






























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