👉 In mathematics and logic, an antiproductively relation is a binary relation that is antisymmetric but not transitive. It means that if a property holds for one element of one set, it does not necessarily hold for another element in the same set. For example, consider the following two relations on the set of all integers: 1. \( \sim \) (antisymmetry): If \( x \sim y \), then \( y \sim x \). 2. \( \ne