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

Parents

Element of

Set universe

Context*

Set universe