Question about Anti Symmetricity
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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
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
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add a comment |
$begingroup$
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
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
$endgroup$
add a comment |
$begingroup$
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
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
$endgroup$
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
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
asked Oct 24 '14 at 4:43
John DoeJohn Doe
1
1
add a comment |
add a comment |
1 Answer
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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*}
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
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1 Answer
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1 Answer
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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*}
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
$endgroup$
add a comment |
$begingroup$
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*}
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
$endgroup$
add a comment |
$begingroup$
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*}
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
$endgroup$
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*}
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
edited Oct 28 '14 at 8:49
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
answered Oct 27 '14 at 14:51
Mick AMick A
8,8702825
8,8702825
add a comment |
add a comment |
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