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?
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.