documentclass{article}
        usepackage{tikz}
        usetikzlibrary{arrows,positioning,shapes,fit,calc}
        pgfdeclarelayer{background}
        pgfsetlayers{background,main}
        begin{document}
        begin{tikzpicture}[
        every node/.style={on grid},
        setA/.style={fill=black, circle, inner sep=1.2pt},
        setC/.style={fill=red, rectangle,inner sep=2pt},
        every fit/.style={draw, fill=white,rectangle,rounded corners=5pt, text width=70pt},>=latex]

         % set A
        node [setA, below = of a,label=left:Initiator] (a) {};
        node[above=of USA,anchor=south] {};

        % set B
        node[inner sep=0pt,right=3cm of a] (x) {Person x};
        node[below = of x] (y) {Person y};
        node[inner sep=0pt,below = of y] (z) {Person z};
        node[above=of x,anchor=south] {$B$};

        % set C
        node[setC,label=right:$m$,right = 3cm of x] (m) {Task a: xxxxxx};
        node[setC,label=right:$n$,below = of m] (n) {Task b: yyyyy};
        node[setC,label=right:$p$,below = of n] (p) {Task c: zzzzz};
        node[above=of m,anchor=south] {$C$};

       % the arrows
       draw[->,shorten >= 3pt] (a) -- node[label=above:$f$] {} (x);
       draw[->,shorten >= 3pt] (b) -- node[label=above:$f$] {} (x);
       draw[->] (c) -- node[label=above:$g$] {} (y);
       draw[->,shorten <= 3pt] (x) -- node[label=above:$h$] {} (m);
       draw[->] (n) -- node[label=above:$u$] {} (y);

       % the boxes around the sets
      begin{pgfonlayer}{background}
      node[fit= (a)  (c) ] {};
      node[fit= (x) (z) ] {};
      node[fit= (m) (p)] {};
      end{pgfonlayer}
      end{tikzpicture}
      end{document}