Sentence:  (i) The identity relation on a set A is an <WSD>antisymmetric</WSD> relation. / (ii) Let R be a relation on the set N of natural numbers defined by /    x R y \Leftrightarrow 'x divides y' for all x, y ∈ N. / This relation is an <WSD>antisymmetric</WSD> relation on N. 
Meaning of the word marked with <WSD> tags:  Having the property that, for any two distinct elements of "S", at least one is not related to the other via "R"; "equivalently", having the property that, for any "x, y" ∈ "S", if both "xRy" and "yRx" then "x"="y".