# Disjoint Sets **A collection of [[Set|sets]] that have no common element.** > [!NOTE] Disjoint Sets > Two [[Set|sets]] $A$ and $B$ are *disjoint* if their [[intersection]] is the [[Set#^5f880b|empty set]]. > $A\cap B=\varnothing$ > ![[DisjointSets.svg|400]] > [!NOTE] Pairwise Disjoint Sets > A collection of sets $A_{1}, A_{2}, A_{3},\dots, A_{k}$ are *pairwise disjoint* if *every pair* of sets is disjoint, that is, > $A_{i}\cap A_{j}=\varnothing$ > for all $i\neq j$. A collection of sets $A_{1}, A_{2}, A_{3}, \dots, A_{k}$ [[partition]] the set $B$ if they are *pairwise disjoint* and their [[union]] is $B$. $A_{1}\cup A_{2}\cup A_{3}\cup\cdots\cup A_{k}=B$