set intersection

#LaTeX

The intersection of two sets is a set operation which returns the set of all elements in both the first set and the second set.

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

A \cap B = {x : x \in A AND x \in B}

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

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

For a finite intersection of sets, we write

S_{1} \cap S_{2} \cap \dots \cap S_{n} = ⋂_{i = 1}^{n} S_{i}

$A$ and $B$ are said to be disjoint if their intersection is empty.
Formally, they are disjoint if $A \cap B = \emptyset$ .

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