Reflexive relation

A relation $R$ on a set $A$ is called a reflexive, if $(a, a) \in R$ for every element $a \in A$, in effect everything loops.

For example:

• Reflexive: $R_1=\{(1,1),(1,2),(3,1),(2,2),(3,3)\}$ on $\{1,2,3\}$ Each element refers to itself.

  digraph G {
  	1->1
    1->2
    3->1
    2->2
    3->3
  }

• Reflexive: $\le$, $\ge$, $=$ Each and every number is lesser than or equal to, greater than or equal or equal to itself.

• Reflexive: ‘divisibility’ on ${\mathbb{N}}^{+}$ Each and every number is divisible by itself.

• Not reflexive: $R_2=\{(1,1),(1,2),(3,1)\}$ on $\{1,2,3\}$ Not every element refers to itself.

  digraph G {
  	1->1
    1->2
    3->1
  }