Venndiagram with 4-sets: how to change the .sty file with modifications

Question

I mention my question at this link Two-set and three-set diagrams: venndiagram package in particular with 3 sets.

\documentclass[a4paper,12pt]{article}
\usepackage{venndiagram}
\begin{document}
\begin{venndiagram3sets}[labelOnlyA={4},labelOnlyB={5},labelOnlyC={7},
labelOnlyAB={3},labelOnlyAC={2},labelOnlyBC={1},labelABC={9},
labelNotABC={8}]
\setpostvennhook{\node[above right] at (venn top right){$|U|=50$};}
\end{venndiagram3sets}
\end{document}

The package venndiagram is old (2018-06-07). Is it possible changed the venndiagram.sty contained in the guide file, putting A, B, C outside the set and construct a diagram with 4 Venn sets that has the same characteristics as a Venn set constructed with 3 circumferences? I am not able to change venndiagram.sty and to contact Nicola L.C. Talbot author of the package here https://www.dickimaw-books.com/latexresources.html and here https://www.goodreads.com/author/show/8503877.Nicola_L_C_Talbot. In fact there is not an email to contact the author. I hope so much for your help also for my first-year students of a scientific high school.

Answer 1

Updated solution

It's not much more complicated to automate this a bit. Here is a command \VennFour that takes one required argument, which is a comma separated list of regions/contents. For example,

\VennFour{a/2, bc/5, bcd/37, abc/33, abcd/3}

will place 2 in the subset that is just A, and 5 in the subset that is B and C but not A or D. Missing regions are left blank. The outer region uses the label o. The label U can be used for the universal set at the top right.

An optional argument can be used for TikZ options that apply to the whole picture. For example,

\VennFour[scale=.8, transform shape]{a/2, bc/5, bcd/37, abc/33, abcd/3}

would scale the entire picture.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\tikzset{ellip/.style={ellipse, draw, thick,
    minimum height=3cm, minimum width=6cm, rotate=#1
}}
\newcommand{\VennFour}[2][]{\begin{tikzpicture}[#1]
    \draw[thick] (-5,-4) rectangle (5,3);
    \coordinate(U) at (5,3.3);
    \node[ellip=-35, label=160:$A$] (A) at (0,0){}; \node[ellip=35, label=20:$B$] (B) at (0,0){};
    \node[ellip=-30, label=270:$C$] (C) at (-1.5,-1){}; \node[ellip=30, label=270:$D$] (D) at (1.5,-1){};
    \coordinate(a)at(-1.6,1.5); \coordinate(b)at(1.6,1.5); \coordinate(c)at(-3.2,0); \coordinate(d)at(3.2,0);
    \coordinate(ab)at(0,.8); \coordinate(cd)at(0,-2.4); \coordinate(ac)at(-2.1,.55);
    \coordinate(bd)at(2.1,.55); \coordinate(ad)at(1.9,-1.3); \coordinate(bc)at(-1.9,-1.3);
    \coordinate(abc)at(-1.1,-.2); \coordinate(abd)at(1.1,-.2); \coordinate(acd)at(.75,-1.7); \coordinate(bcd)at(-.75,-1.7);
    \coordinate(abcd)at(0,-1.1); \coordinate(o)at(0,-3.5);
    \foreach \s/\n in {#2} {\node at (\s){\n};}
\end{tikzpicture}}
\begin{document}
\VennFour{U/$|U|=;?$, a/2, bc/5, bcd/37, abc/33, abcd/3, b/25, c/9, d/12, ac/0, bd/10, ab/23, abd/11, ad/1, acd/6, cd/15, o/4}
\end{document}

Original Solution

I am unfamiliar with the venndiagram package, but I don't see anything in the documentation that indicates its use for more than three sets. In particular, Venn diagrams with more than three sets can't be made from circles, and Venn diagrams with a composite number of sets can't be rotationally symmetric. [See for example, F. Ruskey, C. Savage, and S. Wagon, The search for simple symmetric Venn diagrams, Notices Amer. Math. Soc. 53 (2006) 1304–1312.]

So here is a version drawn from scratch with congruent ellipses.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\tikzset{venn/.style={ellipse, draw, thick,
    minimum height=3cm, minimum width=6cm, rotate=#1
}}
\begin{document}
\begin{tikzpicture}
\draw[thick] (-5,-4) rectangle (5,3)node[above right]{$|U|=n$};
\node[venn=-35, label=160:$A$] (A) at (0,0){};
\node[venn=35, label=20:$B$] (B) at (0,0){};
\node[venn=-30, label=270:$C$] (C) at (-1.5,-1){};
\node[venn=30, label=270:$D$] (D) at (1.5,-1){};
\node at ([shift=(-20:.9)]A.180){1};\node at ([shift=(200:.9)]B.0){2};
\node at ([shift=(-35:1.1)]C.180){3};\node at ([shift=(215:1.1)]D.0){4};
\node at ([shift=(90:.8)]A.center){5};
\node at ([shift=(40:.8)]B.180){8};\node at ([shift=(140:.8)]A.0){7};
\node at ([shift=(-72:1.25)]A.180){6};\node at ([shift=(252:1.25)]B.0){9};
\node at (0,-2.4){10};
\node at (-1.1,-.2){11};\node at (1.1,-.2){12};
\node at (-.8,-1.7){13};\node at (.8,-1.7){14};
\node at (0,-1){15};\node at (0,-3.5){16};
\end{tikzpicture}
\end{document}