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# Reflexivity

## Basic idea

A relation is reflexive if every element is related to itself. One of the three defining properties of an equivalence relation (with symmetry and transitivity).

## Key formulas

* $\forall a \in X.; R(a,a)$
* Equivalently: $\Delta\_X \subseteq R$, where $\Delta\_X = {(a,a) : a\in X}$

A binary relation **R** over a set X is reflexive if it relates every element of X to itself.