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I have read few question posted mathmatics, yet I am still confused... so I do understand this is quiet frequently asked.

If relation = {(1,1)} would this be anti-symmetric and symmetric? I do understand that symmetry means when (a,b) is in set (b,a) should also be in the set. in this case {(a,a),(a,a)} = {(a,a)} and it is also anti-symmetric since there is no another (a,a)?

I think I am contradicting my arguments for symmetry and anti-symmetry but I can't really find any good explanation why this can't be true

Andrés E. Caicedo
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Ben Han
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  • You "can't really find any good explanation why this can't be true" because it's true. It really is both symmetric and antisymmetric. So, antisymmetric does not mean or even imply not symmetric. – BrianO Dec 14 '16 at 03:48

1 Answers1

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The relation ${(1,1)}$ is symmetric because every $(a,b)$ has a matching $(b,a)$. It is also anti-symmetric because the only case where $(a,b) = (b,a)$ is when $ a = b$.

Q the Platypus
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