\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}