While going over my lecture notes for the preparation of exams, I stumbled upon this;
Everything is making sense except the reflexive and anti symmetric relation of natural numbers.
1) By the definition of inequality , we can say that that $(x, x)$ would not appear as an ordered pair.
2)How can it be anti symmetric if the hypothesis $(x,y) \wedge (y, x)$ does not hold? Wouldn't it be meaningless to say anything about the implication if the hypothesis is false?