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Como colorir esses círculos no TikZ?

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Como colorir esses círculos no TikZ?

Como posso colorir a saída deste MWE como na captura de tela?

\documentclass{book}
\usepackage{tikz} 
\begin{document}
\begin{center}
\begin{tikzpicture}
\draw [thick] (3.25,-2) circle (1.5cm)      node[right=.7cm, above=.4cm] {$A$};
\draw [thick] (2.5,-3.5) circle (1.5cm)     node[left=.7cm,] {$B$};
\draw [thick] (4,-3.5) circle (1.5cm)       node[right=.7cm] {$C$};
\draw [thick](0,0) rectangle (6.5,-5.5)     node[left=6cm, above=.3cm] {$M$};
\end{tikzpicture}
\end{center}
\end{document}

insira a descrição da imagem aqui

Responder1

O mais fácil é preencher primeiro os círculos e depois desenhá-los.

\documentclass{book}
\usepackage{tikz}
\begin{document}
\begin{center}
\begin{tikzpicture}
\fill[gray!50] (3.25,-2) circle (1.5cm);
\fill[gray!50] (2.5,-3.5) circle (1.5cm);
\fill[white] (4,-3.5) circle (1.5cm);
\draw [thick] (3.25,-2) circle (1.5cm)      node[right=.7cm, above=.4cm] {$A$};
\draw [thick] (2.5,-3.5) circle (1.5cm)     node[left=.7cm,] {$B$};
\draw [thick] (4,-3.5) circle (1.5cm)       node[right=.7cm] {$C$};
\draw [thick](0,0) rectangle (6.5,-5.5)     node[left=6cm, above=.3cm] {$M$};
\end{tikzpicture}
\end{center}
\end{document}

insira a descrição da imagem aqui

Você pode colorir cada região recortando adequadamente:

\documentclass{book}
\usepackage{tikz}
\begin{document}
\begin{center}
\begin{tikzpicture}
\fill[gray!50] (3.25,-2) circle (1.5cm);
\fill[gray!50] (2.5,-3.5) circle (1.5cm);
\fill[yellow] (4,-3.5) circle (1.5cm);
\begin{scope}
  \clip (2.5,-3.5) circle (1.5cm);
  \fill[blue!50] (3.25,-2) circle (1.5cm);
\end{scope}
\begin{scope}
  \clip (3.25,-2) circle (1.5cm);
  \fill[red!50] (4,-3.5) circle (1.5cm);
\end{scope}
\begin{scope}
  \clip (2.5,-3.5) circle (1.5cm);
  \fill[olive!50] (4,-3.5) circle (1.5cm);
\end{scope}
\begin{scope}
  \clip (2.5,-3.5) circle (1.5cm);
  \clip (3.25,-2) circle (1.5cm);
  \fill[green!50] (4,-3.5) circle (1.5cm);
\end{scope}
\draw [thick] (3.25,-2) circle (1.5cm)      node[right=.7cm, above=.4cm] {$A$};
\draw [thick] (2.5,-3.5) circle (1.5cm)     node[left=.7cm,] {$B$};
\draw [thick] (4,-3.5) circle (1.5cm)       node[right=.7cm] {$C$};
\draw [thick](0,0) rectangle (6.5,-5.5)     node[left=6cm, above=.3cm] {$M$};
\end{tikzpicture}
\end{center}
\end{document}

insira a descrição da imagem aqui

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