# How I draw the symmetrical difference of three sets with Venn diagrams using tikz? [duplicate]

The title says it all, here is the code:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes,backgrounds}
\begin{document}

\def\lcirc2{(-.7,-.5) circle (1cm)}
\def\rcirc2{(.7,-.5) circle (1cm)}
\def\ucirc{(0,.5) circle (1cm)}
\def\rect{(-2.5,-1.8) rectangle (2.5,1.8)}
\begin{tikzpicture}
\begin{scope}
\clip \rcirc2;
\fill[gray] \rcirc2;
\fill[white] \lcirc2;
\fill[gray] \ucirc;
\end{scope}
\begin{scope}
\clip \lcirc2;
\fill[gray] \lcirc2;
\fill[white] \rcirc2;
\end{scope}
\begin{scope}
\clip \ucirc;
\fill[gray] \ucirc;
\end{scope}
\draw \rect;
\draw \lcirc2;
\draw \rcirc2;
\draw \ucirc;
\draw (0,2.1) node {$(A\bigtriangleup B)\bigtriangleup C$};
\draw (0,-.2) node {$X$};
\end{tikzpicture}
\end{document}


I need to shade X gray in addition to each circle without the other. Thanks in advance.

• Avoid using numbers in macro names. In any case, I'm not sure what you're trying to achieve. Would it be possible of you to supply a mock-up version (realized externally) of the desired output? – Alenanno Sep 13 '16 at 17:01
• Please, clarify, what you want to have different. – Heiko Oberdiek Sep 13 '16 at 17:18

The "big triangle" notation often means "symmetric difference". Assuming that's correct, this is a nice example of using the even-odd fill rule:

\documentclass[border=0.4in]{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}

\draw (0, 5.5) node {\Large $(A \bigtriangleup B) \bigtriangleup C$};
\draw[thick] (-5, -3.7) rectangle (5, 4.6);

\fill[even odd rule, gray] \firstcircle \secondcircle \thirdcircle;
\draw[thick] \firstcircle \secondcircle \thirdcircle;

\node[fill = white, shape = circle] (0,0) {$X$};
\end{tikzpicture}
\end{document}


• You can do \fill[even odd rule, gray, draw=black, thick] and collapse the two TikZ instructions into one. Also, I wouldn't make a white circle around X, but rather display X in white ink. – yo' Sep 13 '16 at 18:18
• Pedagogy thrives on verbosity, in my experience. – Derek Sep 13 '16 at 18:50