Intersection (set theory)

Intersection

The intersection of two sets ${\displaystyle A}$ and ${\displaystyle B,}$ represented by circles. ${\displaystyle A\cap B}$ is in red.
Type	Set operation
Field	Set theory
Statement	The intersection of ${\displaystyle A}$ and ${\displaystyle B}$ is the set ${\displaystyle A\cap B}$ of elements that lie in both set ${\displaystyle A}$ and set ${\displaystyle B}$.
Symbolic statement	${\displaystyle A\cap B=\{x:x\in A{\text{ and }}x\in B\}}$

In set theory, the intersection of two sets ${\displaystyle A}$ and ${\displaystyle B,}$ denoted by ${\displaystyle A\cap B,}$^[1] is the set containing all elements of ${\displaystyle A}$ that also belong to ${\displaystyle B}$ or equivalently, all elements of ${\displaystyle B}$ that also belong to ${\displaystyle A.}$^[2]