I would like explain the set theory, but I don't know how to do this.
For example I want to combine them.

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.