Reflexive relation

Y indicates that the column's property is always true for the row's term (at the very left), while ✗ indicates that the property is not guaranteed
in general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric,
is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively.

All definitions tacitly require the homogeneous relation${\displaystyle R}$ be transitive: for all ${\displaystyle a,b,c,}$ if ${\displaystyle aRb}$ and ${\displaystyle bRc}$ then ${\displaystyle aRc.}$
A term's definition may require additional properties that are not listed in this table.

In mathematics, a binary relation${\displaystyle R}$ on a set${\displaystyle X}$ is reflexive if it relates every element of ${\displaystyle X}$ to itself.

An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.