Tikz and Venn Diagrams

Question

I'm trying to draw a Venn diagram for the intersection of {A n B n C} using tikz. Where A: politician, B: lying, C: wicked.

Here's what I have so far but I can't sort the shading out! Any help would be great!

\def\firstcircle{(90:1.75cm) circle (2.5cm)}
  \def\secondcircle{(210:1.75cm) circle (2.5cm)}
  \def\thirdcircle{(330:1.75cm) circle (2.5cm)}
    \begin{tikzpicture}
      \begin{scope}
    \clip \firstcircle \secondcircle;
    \fill[cyan] \thirdcircle;
      \end{scope}
      \begin{scope}
    \clip \thirdcircle \secondcircle;
    \fill[cyan] \firstcircle;
      \end{scope}
      \begin{scope}
    \clip \thirdcircle \firstcircle \secondcircle;
    \fill[cyan] \secondcircle;
      \end{scope}
      \draw \firstcircle node[text=black,above] {$Politician$};
      \draw \secondcircle node [text=black,below left] {$Lying$};
      \draw \thirdcircle node [text=black,below right] {$Wicked$};
    \end{tikzpicture}

On a side note, if anyone has any good documents on learning tikz please let me know! Thank you!

For learning materials, see http://tex.stackexchange.com/questions/15779/materials-for-learning-tikz (And an unrelated note: Don't write $Wicked$ , just Wicked. If you need italics, use \textit{Wicked}.) — Torbjørn T., Dec 21 '16 at 11:47
Is http://tex.stackexchange.com/a/124571/36296 what you want to achieve? — samcarter_is_at_topanswers.xyz, Dec 21 '16 at 12:04
See also http://www.texample.net/tikz/examples/venn-diagram/ — gernot, Dec 21 '16 at 12:09
Also just realised that I have formalised the inference incorrectly: should be $\exists x (Px & Qx & Wx)$. — Andy, Dec 21 '16 at 12:12

Tikz and Venn Diagrams

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