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 ${\displaystyle A\cap B,}$ 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 ${\displaystyle A.}$ The notion of intersection as an algebraic operation with sets as operands has been generalized from geometry, where it is encountered in the case of geometric sets of points, such as individual points, lines (infinite uncountable sets of points), planes, etc.