set union

The union of two sets is a set operation which returns the set of all elements in either the first set or the second set.

Formally,
the union of sets $A$ and $B$ is the operation

where OR represents the logical disjunction, also written $\vee$.

\documentclass[tikz,margin={2cm 0cm}]{standalone}
%
\definecolor{fillcolor}{HTML}{8A5CF5}
%
\begin{document}
\begin{tikzpicture}
	%\path (-3,-2) rectangle (3,2);
	% P
	\fill[fillcolor] (-1,0) circle (1.5);
	% Q
	\fill[fillcolor] (1,0) circle (1.5);
	%
    \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}

For a finite union of sets, we write

The set union is commutative and associative, and distributive over set intersection.