Hi,

I'm learning about relations on sets, and I'm trying to figure out what exactly antisymmetric means. The way we represent a relation is like a adjacency matrix. In my textbook I see that symmetric relation is symmetrical with respect to the diagonal (of the adj. matrix) and that is logical to me, but they also mention that an antisymmetric relation is a relation with members on only one side of the diagonal. This does not make sense to me. I agree that the relations with members only above the diagonal are indeed antisymmetric but not all antisymmetric need to be like that.

Since the condition for antisymmetric is: (x,y)eR and (y,x)eR implies x = y. If I understand this correctly than a relation like this is antisymmetric: R = { (0,0), (1,1), (2,2), (2,0), (1,2) } on set X = { 0, 1, 2 }.

Am I misunderstanding something?