Dibujar el mapeo de elementos para conjuntos en LaTeX

Solución:

Una opción usando TikZ:

documentclass{article}          
usepackage{tikz}
usetikzlibrary{positioning,shapes,fit,arrows}

definecolor{myblue}{RGB}{56,94,141}
begin{document}

begin{tikzpicture}[line width=1pt,>=latex]
sffamily
node (a1) {Anu};
node[below=of a1] (a2) {Ashu};
node[below=of a2] (a3) {Jenny};
node[below=of a3] (a4) {Cathy};

node[right=4cm of a1] (aux1) {};
node[below= 0.5cm of aux1] (b1) {Raaz};
node[below=of b1] (b2) {Jonathan};
node[below=of b2] (b3) {Fred};
node[right=4cm of a4] (aux2) {};

node[shape=ellipse,draw=myblue,minimum size=3cm,fit={(a1) (a4)}] {};
node[shape=ellipse,draw=myblue,minimum size=3cm,fit={(aux1) (aux2)}] {};

node[below=1.5cm of a4,font=color{myblue}Largebfseries] {Domain};
node[below=1.5cm of aux2,font=color{myblue}Largebfseries] {Range};

draw[->,myblue] (a1) -- (b1.170);
draw[->,myblue] (a2) -- (b1.190);
draw[->,myblue] (a3) -- (b2.175);
draw[->,myblue] (a4.20) -- (b2.190);
end{tikzpicture}

end{document}

Otra solución si necesitas adaptar el tamaño del mapa. si desea escalar la imagen, es preferible evitar fit. También es posible que desee dibujar las mismas elipses. En este caso puedes hacer eso

documentclass{article}          
usepackage{tikz}
usetikzlibrary{arrows}

definecolor{myblue}{RGB}{56,94,141}
begin{document}

begin{tikzpicture}[scale=.75]
draw[ultra thick,myblue] (0,0) circle [x radius=1.5cm, y radius=5cm]
                    (6,0) circle [x radius=1.5cm, y radius=5cm];

node[font=color{myblue}Largebfseries] at (0,-6) {Domain};
node[font=color{myblue}Largebfseries] at (6,-6) {Range};  

node (a1)  at (0,3)  {Anu};
node (a2) at (0,1)   {Ashu};
node (a3) at (0,-1)  {Jenny};
node (a4) at (0,-3)  {Cathy};

node[circle] (b1) at (6,2)  {Raaz}; 
 % I used circle to get a fine position of the arrows without a complicated code
node[circle] (b2) at (6,0)  {Jonathan};
node[circle] (b3) at (6,-2) {Fred};

draw[thick,->,myblue] (a1.east) -- (b1);
draw[thick,->,myblue] (a2.east) -- (b1);
draw[thick,->,myblue] (a3.east) -- (b2);
draw[thick,->,myblue] (a4.east) -- (b2);
end{tikzpicture}    
end{document} 

Es posible definir algunos estilos para obtener un mejor código. Es posible usar algunas variables para dibujar automáticamente algunas partes del código.

Actualización 2

Podemos agregar algunos estilos:

documentclass{article}          
usepackage{tikz}
usetikzlibrary{arrows}

definecolor{myblue}{RGB}{56,94,141}
newcommandxsetpos{6}

begin{document}

begin{tikzpicture}[scale=.75,
                    arrow/.style={thick,->,myblue},
                    set name/.style={font=color{myblue}Largebfseriessf},
                    set/.style={ultra thick,myblue},
                    every node/.style={circle},
                    font=sf
                    ]
draw[set] (0,0) circle [x radius=1.5cm, y radius=5cm]
           (xsetpos,0) circle [x radius=1.5cm, y radius=5cm];

node[set name] at (0,-6) {Domain};
node[set name] at (xsetpos,-6) {Range};  

node (a1) at (0,3)  {Anu};
node (a2) at (0,1)  {Ashu};
node (a3) at (0,-1) {Jenny};
node (a4) at (0,-3) {Cathy};

node (b1) at (xsetpos,2)  {Raaz};
node (b2) at (xsetpos,0)  {Jonathan};
node (b3) at (xsetpos,-2) {Fred}; 

begin{scope}[arrow]
  draw (a1.east) -- (b1);
  draw (a2.east) -- (b1);
  draw (a3.east) -- (b2);
  draw (a4.east) -- (b2); 
end{scope}

end{tikzpicture}    
end{document} 

No es necesario utilizar coordenadas absolutas, que complican las cosas:

documentclass[dvipsnames]{article}
usepackage{pst-node}
begin{document}
begin{center}
FindFathersMap

defarraystretch{2 }
tabular{[email protected]{hspace{3cm}}c}
psovalbox[fillstyle=solid,fillcolor=blue!10]{%
tabular{c}    % left names
    rnode[r]{Anu}{Anu}\
    rnode[r]{Ashu}{Ashu}\
    rnode[r]{Jenny}{Jenny}\
    rnode[r]{Cathy}{Cathy}
endtabular}
&
psovalbox[fillstyle=solid,fillcolor=blue!10]{%
tabular{c}    % right names
    rnode[l]{Raaz}{Raaz}\
    rnode[l]{Jonathan}{Jonathan}\
    rnode[l]{Fred}{Fred}
endtabular}
\
textcolor{NavyBlue}{bfseries Domain} & textcolor{NavyBlue}{bfseries Range}
endtabular
 psset{linecolor=NavyBlue,nodesep=6pt,arrows=->,arrowscale=2}
 ncline{Anu}{Raaz}    ncline{Ashu}{Raaz}   ncline{Jenny}{Jonathan}   ncline{Cathy}{Jonathan}
end{center}
end{document}

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