👉 In mathematics, an equivalence relation is a binary relation on a set S that is reflexive (every element of S is related to itself), symmetric (for every x and y in S, if xRy then yRx), and transitive (for every x, y, z in S, if xRy and yRz then xRz). These properties ensure the relation is a symmetry preserving binary relation. For example, consider two sets A and B. The set of all