Set Complement

up:: 020 MOC Mathematics

Given sets $S,X$, we define the complement of $S$ with respect to $X$ as

$$X\setminus S=\{x\in X\mid x\notin S\}$$

In particular cases in which $S\subseteq X$, one denotes this complement as $S^c$, implicitly assuming it is its complement with its superset ─ which is usually the entire base space.

Properties

• Set Complements flip subset ordering