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This is an example exercise from my Algebra class:

Find the antisymmetric closure of $$R=\{(1,2),(1,3),(2,2),(2,1)\}$$ on $$\{1,2,3\}$$

I don't see it explicitly defined in the lecture notes and I couldn't find much information about Antisymmetric Closure online.

I sort of understand Reflexive, Symmetric and Transitive Closure, but not Antisymmetric Closure. How is it defined and how can I find it?

ChocolateOverflow
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    Symmetry, transitivity and reflexivity are all about pairs that should exist, and therefore the relevant closures are about adding those pairs. Antisymmetry is about pairs that shouldn't exist, and I don't know a canonical way to make that happen. – Arthur Jan 16 '20 at 10:22
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    To be honest, seeing how I can't find anything good that mentions it, I see a possibility that my professor might have mistypped something... – ChocolateOverflow Jan 16 '20 at 10:26

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