The complement of $U$ is the set $U^{\textsf{c}}$ defined by
\begin{align*} U^{\textsf{c}} & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}X\setminus U\\ & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ a\in X\ \middle |\ a\not\in U\webright\} .\end{align*}
