[Tex/LaTex] Get Venn diagram of a complement of (A intersection B) union (A union B)^complement

Question

This is what my venn diagram looks like currently. I want it to look something like this.

This is what I have so far

    \documentclass[12pt]{article}

    \usepackage{amsmath}
    \usepackage[margin=0.5in]{geometry}
    \usepackage{tikz}
    \setlength\parindent{0pt}
    \begin{tikzpicture}[line width = 2pt] % For some thicker lines
    
% Local variables to position the circles and bounding box
    \coordinate (X) at (-0.44\textwidth,-0.15\textheight);
    \coordinate (Y) at (+0.44\textwidth,+0.15\textheight);
    \coordinate (A) at (-0.7in,0);
    \coordinate (B) at (+0.7in,0);

    % To shade the correct part of the Venn diagram
    \begin{scope}
      \clip
        (B) circle (1in);
      \fill
        [gray!50] (A) circle (1in);
    \end{scope}

    \begin{scope}
      \clip
      
    \end{scope}

    \draw (X) rectangle (Y) node[below left] {\huge $U$};
    \draw (A) circle (1in)  node {\huge $A$}; % Draw a cirle of radius 1in at A
    \draw (B) circle (1in)  node {\huge $B$}; % Draw a cirle of radius 1in at B
  \end{tikzpicture}
  \centerline{Venn diagram of}
  \centerline{$(A \cap B) \cup (A \cup B)^c $}

How do I fix it?

Answer 1

A short code with pstricks:

\documentclass[svgnames, border=6pt]{standalone}
\usepackage{pst-eucl}

\begin{document}

\begin{pspicture}(-5.5,-2.5)(5.5,2.5)
\psset{fillstyle=solid}
\psframe[fillstyle=solid, fillcolor=Gainsboro](-5.5,-2.5)(5.5,2.5)
\pstGeonode[PointSymbol=none, PointName=](-1.5,0){A}(1.5,0){B}(-1.5,2){C}(1.5,2){D}
\psset{fillcolor=white}
\pscircle(A){2}\pscircle(B){2}
\rput(A){$A$}\rput(B){$B$}
\pstInterCC{A}{C}{B}{D}{M}{N}
\pscustom[fillcolor=LemonChiffon]{\pstArcOAB{B}{M}{N}\pstArcOAB{A}{N}{M}}
\end{pspicture}

\end{document}