## Intersection

### Set

context | $X,Y\in\mathfrak U$ |

definiendum | $ x\in X \cap Y $ |

postulate | $ x\in X \cap Y \Leftrightarrow (x\in X\land x\in Y) $ |

### Discussion

$ X \cap Y $ is commutative and idempotent.

The intersection and union are associative and distributive with respect to another.

#### Reference

Wikipedia: Intersection