What I am looking to do is to connect particular intersections of a venn diagram in 3 variables, with arrows. So for example, I manipulated the code here: Venn Diagrams and shaded the intersections according to
$(A \wedge B \vee A \wedge C \vee B \wedge C) \wedge \neg (A \wedge B \wedge C)$
What I can't figure out how to do is to label these intersections and connect them with arrows.
Now, I realize the first code sample has a point in it which would correspond to the intersection of A,B, and C - but in case I would like to connect it in the future, I left it in there.
I can get the code to work to display, for example, derived from an answered question here
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}
% \node (G) [below right=1cm and 0cm of E] {$G = \{4,5,6,7\}$};
\node (z) {$Z$};
\node (xyz) [below=.8 of z] {$X \times Y$};
\node (x) [below left=.578cm and 1cm of xyz] {$X$};
\node (y) [below right=.578cm and 1cm of xyz] {$Y$};
\draw[<->] (z) to node [sloped, above] {$ $} (y);
\draw[<->] (x) to node [sloped, above] {$ $} (z);
\draw[<->] (y) to node [sloped, above] {$ $} (x);
\draw[-] (z) to node {$ $} (xyz);
\draw[-] (xyz) to node [below] {$\pi_X$} (x);
\draw[->] (xyz) to node [below] {$\pi_Y$} (y);
\end{tikzpicture}
\end{document}
as well as:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\def\firstcircle{(0,0) circle (1.5cm)}
\def\secondcircle{(60:2.1cm) circle (1.5cm)}
\def\thirdcircle{(0:2.1cm) circle (1.5cm)}
\begin{figure}[htb]
\begin{tikzpicture}
\draw \firstcircle node[below] {$A$};
\draw \secondcircle node [above] {$B$};
\draw \thirdcircle node [below] {$C$};
\begin{scope}
\clip \firstcircle;
\fill[pink] \secondcircle;
\end{scope}
\begin{scope}
\clip \secondcircle;
\fill[pink] \thirdcircle;
\end{scope}
\begin{scope}
\clip \firstcircle;
\fill[pink] \thirdcircle;
\end{scope}
\begin{scope}
\clip \firstcircle;
\clip \secondcircle;
\fill[white] \thirdcircle;
\end{scope}
\end{tikzpicture}
\end{figure}
\end{document}
Thanks for any help,
Brian