set difference

#LaTeX

The set difference of sets $B$ and $A$ , also the relative complement of $A$ with respect to $B$ , is the set operation which returns the set of elements in $B$ that are not in $A$ .

Formally,
the set difference of $B$ and $A$ is written

B ∖ A = {x : x \in B AND x \notin A}

where AND is the logical conjunction, also written $\land$ .

\documentclass[tikz,margin={2cm 0cm}]{standalone}
%
\definecolor{fillcolor}{HTML}{8A5CF5}
%
\begin{document}
\begin{tikzpicture}
    \begin{scope}[even odd rule]
        \clip (2.5,-1.5) rectangle (0,1.5);
        \fill[fillcolor] (-1,0) circle (1.5) (1,0) circle (1.5);
    \end{scope}
    \draw (-1,0) circle (1.5);
    \draw (1,0) circle (1.5);
    \node at (-1.25,0) {$A$};
    \node at (1.25,0) {$B$};
\end{tikzpicture}
\end{document}

Let $U$ be a set that contains all the elements under study (the universe or universal set);
the absolute complement (or simply set complement) is the relative complement of $A$ in $U$ :

A^{∁} = U ∖ A = {x \in U : x \notin A}