Equivalence relation

A relation $R$ on a set $A$ is called an equivalence relation if it is: ?

• reflexive: everything loops
• symmetric: all arrows come in pairs
• transitive: every 2-step journey must be also done in 1-step

For example:

• $=$ on any set
• $\{(x,y)\in \mathbb{Z}\times \mathbb{Z}|x-y\text{ is divisble by }4\}$ on $\mathbb{Z}$