A relation R is antisYmmetric if, for all x and Y, x R Y and Y R x => x == Y. I.e. no two different elements are mutuallY related. Partial orders and total orders are antisYmmetric. If R is also sYmmetric, i.e. x R Y => Y R x then x R Y => x == Y I.e. different elements are not related. (1995-04-18)