Symmetric and Transitive Relation is not necessarily Reflexive/Examples

Examples of Use of Symmetric and Transitive Relation is not necessarily Reflexive

Subset of Cartesian Plane

The subset of the Cartesian plane defined as:

$\RR := \set {\tuple {x, y} \in \R^2: -1 \le x \le 1, -1 \le y \le 1}$

determines a relation on $\R^2$ which is symmetric and transitive but not reflexive.