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\documentclass{article}
\usepackage{venndiagram}
\begin{document}
$ \mathcal{U} \setminus (\mathcal{A} \cup \mathcal{B} \cup
\mathcal{C})$:
\begin{venndiagram3sets}
\fillNotABC
\end{venndiagram3sets}
$ \mathcal{B} \setminus \mathcal{A} $
\begin{venndiagram2sets}
\fillOnlyB
\end{venndiagram2sets}
Using the labels:
\begin{venndiagram3sets}[labelOnlyA={1},labelOnlyB={2},labelOnlyC={3},
labelOnlyAB={4},labelOnlyAC={5},labelOnlyBC={6},labelABC={7},
labelNotABC={8}]
\end{venndiagram3sets}
Annotating the diagram:
\begin{venndiagram3sets}[labelOnlyA={1},labelOnlyB={2},labelOnlyC={3},
labelOnlyAB={4},labelOnlyAC={5},labelOnlyBC={6},labelABC={7},
labelNotABC={8}]
\setpostvennhook
{
\draw[<-] (labelA) -- ++(135:3cm) node[above] {Students who eat artichokes};
\draw[<-] (labelB) -- ++(45:3cm) node[above] {Students who eat broccoli};
\draw[<-] (labelC) -- ++(-90:3cm) node[below] {Students who eat carrots};
\draw[<-] (labelABC) -- ++(0:3cm)
node[right,text width=4cm,align=flush left]
{7 students eat artichokes, broccoli and carrots};
\draw[<-] (labelNotABC) -- ++(-135:3cm)
node[below,text width=4cm,align=flush left]
{8 students don't eat artichokes, broccoli or carrots};
}
\end{venndiagram3sets}
\end{document}
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