Properties of relations (symmetry and anti-symmetry)

Question

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

Answer 1

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$.