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My included graphics are too blurry so I decided to find out, how to draw the following four graphics in TikZ. I never really worked with TikZ, so can someone explain how to draw such graphics?

Visualization of relations

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You should add a Minimal Working Example and say what is exactly your problem or what you don't know to do. – Manuel Dec 18 '12 at 1:37
You are welcome but what exactly is the question? – percusse Dec 18 '12 at 1:37
@percusse: Added the question. – Christian Ivicevic Dec 18 '12 at 1:43
up vote 10 down vote accepted

Here's one possibility:


  \node[draw,minimum width=3cm,minimum height=3cm] (#1) {};
  \draw[->] (#1.east) -- +(10pt,0) node[label=below :$\mathbb{R}$] {};
  \draw (#1.west) -- +(-10pt,0);
  \draw[->] (#1.north) -- +(0,10pt) node[label=right :$\mathbb{R}$] {};
  \draw (#1.south) -- +(0,-10pt);

\draw (a.north west)  -- node[auto,swap,midway] {$R_1$} +(1.5cm,-1.5cm) -- (a.north east);
\draw (b.north east)  -- node[auto,swap,midway] {$R_1^{-1}$} +(-1.5cm,-1.5cm) -- (b.south east);
\filldraw[draw=black,fill=blue!20] (c.north east)  -- (c.north west) -- (c.south west) -- cycle;
\node at ([xshift=15pt,yshift=-15pt]c.north west) {$R_2$};
\filldraw[draw=black,fill=blue!20] (d.north east)  -- (d.south west) -- (d.south east) -- cycle;
\node at ([xshift=-15pt,yshift=15pt]d.south east) {$R_2^{-1}$};


enter image description here

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