Universal set in Venn diagrams

Question

I have not used the venndiagram package before. I have tried to read the manual, but could not find an answer to how to make the universal set box fit for any number of elements.

Here is what I have so far:

    \documentclass{book}
\usepackage{newfile}
 \usepackage{amsmath}
 \usepackage{xifthen}
 \usepackage{enumitem}
 \usepackage{multicol}
 \usepackage{lipsum}
 \usepackage{multirow}
 \usepackage{blindtext}
 \usepackage{amsfonts}
 \usepackage{booktabs}
 \usepackage{longtable}
 \usepackage{makecell}
 \usepackage{cancel}
 \usepackage{tikz}
 \usetikzlibrary{tikzmark,shapes.misc}
 \usepackage{venndiagram}
 \usetikzlibrary{fit}
 \usepackage[left=2.00cm, right=1.00cm, top=3.00cm, bottom=3.00cm]{geometry}
\usepackage{cellspace}
%------------------------------------
%-----------------------------------
\renewcommand\theadfont{\bfseries}
\usepackage{verbatim}
%\usepackage[active,tightpage]{preview}
%\PreviewEnvironment{tikzpicture}
%\setlength\PreviewBorder{5pt}%
\def\firstcircle{(0,0) circle (1.5cm)}
\def\secondcircle{(0:2cm) circle (1.5cm)}
\colorlet{circle edge}{blue!50}
\colorlet{circle area}{blue!20}
\tikzset{filled/.style={fill=circle area, draw=circle edge, thick},
    outline/.style={draw=circle edge, thick}}
\setlength{\parskip}{5mm}
\begin{document}
\chapter{Sets and Venn Diagrams}
 \section{Sets}


A set is a specific group of numbers or items from a list.          The items in this set   (the list list), are called Elements.\
Sets can be written in a few different ways - eg the set $A$      can be  written as,  $A={1,8,27,64}$, $A={Cube : numbers    <100}$ and  $A={x:x :is :a :cube :number   :less :than    :100}$
 \section{Set Notiation}


If we take the natural numbers, $\mathbb{N} \leq10$
\begin{tabular}{|c|c|c|c|}
  \hline
   Sybmol             & Name                       & Example                                                                  & Explanation\
  \hline
 ${}$                  & Set                           &   \thead{$A={1,3}$ \ $B={2,3,9}$ \ $C={3,9}$} &  Collection   of objects or items\
 \hline
 $\cap$                & intersect                   & $A \cap    B = {3}$                                                  &  3    belongs to both sets $A$ and $B$ \
 \hline
 $\cup$                & Union                        & $A \cup    B = {1,2,3,9}$                                         & The       elements belong to both $A$ and $B$ \
 \hline
 $\xi$                    & The universal set     & $\xi=\ {4,5,6,7,8,10}$                                             & All     the elements not in the sets  \
 \hline
 $\subset$            & Proper subset          & \thead{${1}    \cup A$  \ $C \cup B$}                     & A set is contained in    another set \
 \hline
 $\subseteq$        &Subest                      & $\thead{B   \subseteq A \ {1,3}}$                          &  A set that is     contained in or equal to another set\
 \hline
 $\not \subseteq$ & Not a proper subset & ${1,3}$                                                                  & A set the is not contained in another set \
 \hline
 $\supset$            & Superset                  & $B  \supset C$                                                     &  Set $B$   includes set $C$\
 \hline
 $\epsilon$           & is a member of         & $3 \epsilon  A$                                                     & $3$ is in  the set $A$\
 \hline
 $\not\epsilon$     & is not a member of   & $4 \not\epsilon A $                                                  & $4$ is not in   the set $A $\
 \hline
\end{tabular}
%--------------------------Problem code is here------------------%
my attempt
 \begin{venndiagram3sets}[labelOnlyA={1},labelOnlyB=  {2},labelOnlyC={}, labelOnlyAB={},labelOnlyAC={},labelOnlyBC=  {9},labelABC={3}, labelNotABC={4,5,6,7,8,10}]
     \end{venndiagram3sets} %My Attempt
%------------------------------------%
First suggestion
 \begin{venndiagram3sets}[
   labelOnlyA={1},
   labelOnlyB={2},
   labelOnlyC={},
   labelOnlyAB= {},
   labelOnlyAC={},
   labelOnlyBC={9},
   labelABC={3},
   labelNotABC={4,5,6,7,8,10},
    showframe=false,
 ]
  \setpostvennhook{
   \node[below left] at (venn top right) {(\mathcal{E})};
   \node[fit=(venn top right) (venn bottom left)   (labelNotABC),draw] {};
 }
 \end{venndiagram3sets} % second attempt
%--------------------------------------------%
  Second suggestion
  \fbox{\begin{venndiagram3sets}[showframe=false,labelOnlyA= {1},labelOnlyB={2},labelOnlyC={}, labelOnlyAB= {},labelOnlyAC= {},labelOnlyBC={9},labelABC={3}, labelNotABC={$\xi$ \ {4,5,6,7,8,10}}]
     \end{venndiagram3sets}} %third attempt
%-----------And ends here----------------------------------%
%Diagrams
 \section{diagrams}

 % Definition of circles


\begin{tabular}{cc}
  % Set A and B
 \begin{tikzpicture}
     \begin{scope}
          \clip \firstcircle;
          \fill[filled] \secondcircle;
     \end{scope}
     \draw[outline] \firstcircle node {$A$};
     \draw[outline] \secondcircle node {$B$};
     \node[anchor=south] at (current bounding box.north) {$A \cap B$};
 \end{tikzpicture}
&
  %Set A or B but not (A and B) also known a A xor B
  \begin{tikzpicture}
     \draw[filled, even odd rule] \firstcircle node {$A$}
                                  \secondcircle node{$B$};
     \node[anchor=south] at (current bounding box.north)  {$\overline{A \cap B}$};
  \end{tikzpicture}
% Set A or B
 \begin{tikzpicture}
      \draw[filled] \firstcircle node {$A$}
                   \secondcircle node {$B$};
      \node[anchor=south] at (current bounding box.north) {$A \cup B$};
 \end{tikzpicture}\
% Set A but not B
 \begin{tikzpicture}
     \begin{scope}
         \clip \firstcircle;
         \draw[filled, even odd rule] \firstcircle node {$A$}
                                      \secondcircle;
     \end{scope}
     \draw[outline] \firstcircle
                    \secondcircle node {$B$};
     \node[anchor=south] at (current bounding box.north) {$A - B$};
     \end{tikzpicture}
&
 % Set B but not A
 \begin{tikzpicture}
     \begin{scope}
         \clip \secondcircle;
         \draw[filled, even odd rule] \firstcircle
                                      \secondcircle node {$B$};
     \end{scope}
     \draw[outline] \firstcircle node {$A$}
                    \secondcircle;
     \node[anchor=south] at (current bounding box.north) {$B -  A$};
 \end{tikzpicture}\
\end{tabular}
\end{document}

I have edited this to provide all the code for my page incase anything is causing my problems. sorry for the long code.

Answer 1

I am not sure what you want to achieve, but I think you want to place the label for the universal set at a place where it does not intersect with the surrounding box.

This answer explains how you can use the macro \setpostvennhook to customize the position of the labels. The manual of the package further adds that there are coordinates in all four corners of the venn diagram, which you can use to align the labels. You can also use the options vgap or hgap to increase the margin between the circles and the outer box.

Of course, if the contents of the label is too long, it will eventually "crash" into the right border of the surrounding box ...

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usepackage{venndiagram}
\begin{document}
\begin{venndiagram3sets}[labelOnlyA={1}, labelOnlyB={2}, labelOnlyC={}, labelOnlyAB= {}, labelOnlyAC={}, labelOnlyBC={9}, labelABC={3}, vgap=.75cm]
\setpostvennhook{
    \node[anchor=south west] at (venn bottom left) {$\xi$ \{4,5,6,7,8,10\}};
}


\end{venndiagram3sets}
\end{document}

Answer 2

You can use the \setpostvennhook to insert arbitrary TikZ code to be drawn after the venn diagram is constructed. Since the default size of the frame doesn't take into account the labels, it can be redrawn here taking that into account. Specifically, using the fit library then a node can be drawn that is guaranteed to encompass the diagram and the non-ABC label. Note that you need the option showframe=false to avoid drawing the original universal set frame.

I've also make a couple of other changes:

1. The elements not in the sets A,B,C shouldn't be enclosed in braces. Technically, writing \{4,5,6,7,8,10\} indicates that the outer region contains one element which is the set containing 4,5,6,7,8,10. I presume that what you want to indicate is that the outer region itself contains those numbers.
2. To avoid the symbol for the universal set getting confused with the elements, I've used the \setpostvennhook to place its symbol in the top right corner (which, I think, is a more standard place for it to be). I've also used \mathcal{E} rather than \xi.

\documentclass{book}
%\url{https://tex.stackexchange.com/q/653355/86}
\usepackage{tikz}
\usepackage{venndiagram}
\usetikzlibrary{fit}
\usepackage[left=2.00cm, right=1.00cm, top=3.00cm, bottom=3.00cm]{geometry}
\begin{document}
\begin{venndiagram3sets}[
  labelOnlyA={1},
  labelOnlyB={2},
  labelOnlyC={},
  labelOnlyAB= {},
  labelOnlyAC={},
  labelOnlyBC={9},
  labelABC={3},
  labelNotABC={4,5,6,7,8,10},
  showframe=false,
]
\setpostvennhook{
  \node[below left] at (venn top right) {(\mathcal{E})};
  \node[fit=(venn top right) (venn bottom left) (labelNotABC),draw] {};
}
\end{venndiagram3sets}
\end{document}

Answer 3

Instead of letting the venndiagram package draw the rectangle, you could wrap it into an \fbox

\documentclass{book}
\usepackage{makecell}
\usepackage{tikz}
\usepackage{venndiagram}
\renewcommand\theadfont{\bfseries}
\usepackage{cellspace}
\usepackage{tikz}
\usepackage{verbatim}
\usepackage[left=2.00cm, right=1.00cm, top=3.00cm, bottom=3.00cm]{geometry}
\def\firstcircle{(0,0) circle (1.5cm)}
\def\secondcircle{(0:2cm) circle (1.5cm)}
\colorlet{circle edge}{blue!50}
\colorlet{circle area}{blue!20}
\tikzset{filled/.style={fill=circle area, draw=circle edge, thick},
     outline/.style={draw=circle edge, thick}}
\setlength{\parskip}{5mm}
\begin{document}
\fbox{\begin{venndiagram3sets}[showframe=false,labelOnlyA={1},labelOnlyB={2},labelOnlyC={}, labelOnlyAB= {},labelOnlyAC={},labelOnlyBC={9},labelABC={3}, labelNotABC={$\xi$ {4,5,6,7,8,10}}]
    \end{venndiagram3sets}}
    \end{document}