Complement

A complement of a set $A$ is defined relative to a fixed ambient set (universe) $U$ with $A\subseteq U$. The complement of $A$ in $U$ is

Equivalently, $A^{c}$ is the set difference $U\setminus A$. Complements interact with union and intersection through De Morgan’s laws.

Examples:

• If $U=\{1,2,3,4\}$ and $A=\{1,4\}$, then $A^{c}=\{2,3\}$.
• If $U=\mathbb{R}$ and $A=\{x\in\mathbb{R}: x\ge 0\}$, then $A^{c}=\{x\in\mathbb{R}: x<0\}$.