# Intersection (set theory)

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In set theory, the intersection of two sets $A,B$ is the set of all elements in $A$ that also belong in $B$ .

Definition

Given two sets A and B,
$A\cap B=\{x|x\in A\and x\in B\}$

If the intersection of two sets is empty, then the two sets are disjoint.

## Example

Suppose $A=\{a,b,f,g\}$ and $B=\{b,c,d,g\}$ .

$A\cap B=\{b,g\}$