Symbols:C/Set Complement

Set Complement

$\map \complement S$ or $\map \CC S$

The set complement (or, when the context is established, just complement) of a set $S$ in a universe $\mathbb U$ is defined as:

$\map \complement S = \relcomp {\mathbb U} S = \mathbb U \setminus S$

See the definition of Relative Complement for the definition of $\relcomp {\mathbb U} S$.

The $\LaTeX$ code for \(\map \complement S\) is \map \complement S .

The $\LaTeX$ code for \(\map \CC S\) is \map \CC S .

Prime Notation

$S'$

The set complement can be defined and denoted:

$S' := \mathbb U \setminus S$

The $\LaTeX$ code for \(S'\) is S' .

Overline Notation

$\overline S$

The set complement can be defined and denoted:

$\overline S := \mathbb U \setminus S$

The $\LaTeX$ code for \(\overline S\) is \overline S .