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I would like explain the set theory, but I don't know how to do this.

For example I want to combine them.

IMAGE OF THE URL

This is my inital code:

\documentclass{beamer} %contains the document size %handout for better printing results
% use [draft] instead handout and it compiles faster
\usepackage{beamerthemesplit}
\usetheme{PaloAlto}
\usecolortheme{crane} %http://www.hartwork.org/beamer-theme-matrix/

%\setbeamercovered{transparent} %transparente overlay
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}

\usepackage{pgfpages}
\pgfpagesuselayout{resize to}[a4paper,border shrink=5mm,landscape] %for printing, beamer has a differnt paper size.
\keywords{Learning Latex}
%\logo{\pgfimage[width=1cm,height=0,5cm]{TU Graz}}
\setbeamertemplate{footline}[frame number] %if you have a lots of frames, it is better do not show the pagenumbers. 

\newtheorem*{com}{Comment}


\usepackage[UKenglish]{babel}
\usepackage[utf8]{inputenc}

\definecolor{BlueLUH}{cmyk}{1.0,0.7,0,0.9}


\begin{document}
%-------------------------------------------------------------
\def\firstcircle{(0,0) circle (2cm)}
\def\secondcircle{(0:5cm) circle (2cm)}

\colorlet{edge}{BlueLUH!20!white}
\colorlet{area}{BlueLUH!80!black!20}

\tikzset %\tikzset{every path/.style={}}
{filled/.style= {fill=area, draw=edge, thick}, 
outline/.style={draw=edge, thick}}
%-------------------------------------------------------------

\date{\today}


\frame{\titlepage}

\part[par]{Documentclass beamer}  %at lectures with several presentations 

\begin{abstract}
In this short presention, I explain you the set theory.
\end{abstract}

\frame{\frametitle{Table of contents}\tableofcontents}

\section{Circles}
\begin{frame}
\uncover<1-2>
{\begin{tikzpicture}
 \draw[filled] 
 \firstcircle node {$A$};
\end{tikzpicture}
}

\uncover<2-2>
{\begin{tikzpicture}
 \draw[filled] 
 \secondcircle node {$B$};
\end{tikzpicture}
}

\only<3-3>
{\begin{tikzpicture}
    \begin{scope}
        \clip \firstcircle;
        \fill[filled] \secondcircle;
    \end{scope}
    \draw[outline] \firstcircle node  {$A$};
    \draw[outline] \secondcircle node {$B$};
\end{tikzpicture}
}
\end{frame}

\section{Outro}
\frame{
\begin{center}
\huge Thank you!
\end{center}
}

\end{document}

I edited it, but it still doesn't work:

\section{Circles}
\begin{frame}
\begin{tikzpicture}
\uncover<1-2>{
\draw[filled] 
\firstcircle node[name=A] {$A$};
}
\uncover<2>
{
\draw[filled,opacity=0.8, xshift = 2.5cm],  
\secondcircle node[name=B] {$B$};
\path [name intersections = {of = firstcircle and secondcircle } ] (intersection-1) -- (intersection-2) node [pos=0.5] {$A \cap B$};
}
\uncover<3>
{
\draw[filled,opacity=0.8],  
\secondcircle node[name=B] {$B$};
\path [name intersections = {of = firstcircle and secondcircle } ] (intersection-1) -- (intersection-2) node [pos=0.5] {$A \cap B$};
}
\end{tikzpicture}
\end{frame}

Infact I see this error:

tikz Error: giving up on this path did you forget a semicolon? \end{frame} ! Package pgf Error: No shape named intersection-1 is known. ! Package tikz Error: I do not know the path named `secondcircle'.

Perhaps you misspelt it.

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