What if union of disjoint sets results in universal set?

What if union of disjoint sets results in universal set?

• I have a question related to set theory. If $A_1,A_2,A_3\dots, A_n$ belongs to universal set $U$, and if all of the sets are disjoint i.e. $A_i \cap A_j = \emptyset$ for all $i$ and $j$. And If their union equals to Universal set i.e. $A_1 \cup A_2 \cup \dots A_n = U $ = Universal set. What is such situation called?

• Answer:

  If every $A_i$ is nonempty, you have described a http://en.wikipedia.org/wiki/Partition_of_a_set of the set $U$. The definition holds for any set, not just for the current universal set. If the union of disjoint (non-empty) sets equal any set $X$, we say in the same way that we have a partition of $X$.