Complement

Let $A$ be a set with a universal set $U$. The complement of $A$, denoted $\overline{A}$, is the set $\overline{A}=U-A$. It contains all elements in the universal set that are not in $A$.

Context

Complements are used extensively in probability and set theory. For example, if $U=\{1,2,3,4,5\}$ and $A=\{1,2\}$, then $\overline{A}=\{3,4,5\}$. In probability, $P(\overline{A})=1-P(A)$, which is often easier to compute than $P(A)$ directly.

See Also

• set
• universal set
• subset
• Empty Set