# Definition:Ring of Sets/Definition 1

A ring of sets $\mathcal R$ is a system of sets with the following properties:
 $(RS \, 1_1)$ $:$ Non-Empty: $\displaystyle \mathcal R \ne \varnothing$ $(RS \, 2_1)$ $:$ Closure under Intersection: $\displaystyle \forall A, B \in \mathcal R:$ $\displaystyle A \cap B \in \mathcal R$ $(RS \, 3_1)$ $:$ Closure under Symmetric Difference: $\displaystyle \forall A, B \in \mathcal R:$ $\displaystyle A * B \in \mathcal R$