Is Identity Relation Symmetric?

Is Identity Relation Symmetric? The identity relation consists of ordered pairs of the form (a,a), where a∈A. In other words, aRb if and only if a=b. It is reflexive (hence not irreflexive), symmetric, antisymmetric, and transitive. Are identity relations equivalence? Thus Identity relation is always an Equivalence Relation. Is identity relation a transitive? Transitivity is

Can A Relation Be Both Reflexive And Irreflexive?

Can A Relation Be Both Reflexive And Irreflexive? That is, a relation on a set may be both reflexive and irreflexive or it may be neither. The same is true for the symmetric and antisymmetric properties, as well as the symmetric and asymmetric properties. Can something be reflexive and anti-reflexive? A binary relation over some