# Intersection (set theory)

In mathematics, 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]

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