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I have a set put into matrics form, if

{ (a,a), (a,b), (a,c), (a,d), (b,a), (b,b), (b,c), (b,d), (c,a), (c,b), (c,c), (c,d), (d,a), (d,b), (d,c), (d,d) }

And the 4 relations: Reflexive, Symmetric, AntiSymmetric, Transitive.

Symmetric would be the pair's inverse of each other eg, (b,a) & (a,b)

Then AntiSymmetric would be the diagonal line starting from (a,a) ending at (d,d) as for (x,y), x = y

But if AntiSymmetric is the diagonal from (a,a) to (d,d), does that means that anti symmetric and reflexive is the same thing for this set?

Asaf Karagila
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LuxuryWaffles
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    "Reflexive, symmetric, antisymmetric, transitive" are not 4 relations. Each of them is a property that some but not all relations have. There are many different reflexive relations, many different symmetric ones, and some that are at once reflexive and symmetric, and so on. – hmakholm left over Monica Apr 17 '17 at 16:39

1 Answers1

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No, the relation is not anti-symmetric.
Anti-simmetry is $(a,b) \in R$ and $(b,a) \in R$ implies that $a=b$.
Your relation is not like that.

amrsa
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