\documentclass{article}

\usepackage{tikz}

\begin{document}

The following is an example Hasse Diagram drawn using pgf/TikZ:

\begin{center}

    \begin{tikzpicture}[scale=.85]

    \draw[fill] (0,0) circle (.05cm) node[right] {$1$};

    \draw (0,0) -- (-2,2);
    \draw (0,0) -- (0,2);
    \draw (0,0) -- (2,2);

    \draw[fill] (-2,2) circle (.05cm) node[right] {$2$};
    \draw (-2,2) -- (-3,4);
    \draw (-2,2) -- (-1,4);
    \draw (-2,2) -- (1,4);
    \draw[fill] (0,2) circle (.05cm) node[right] {$3$};
    \draw (0,2) -- (-1,4);
    \draw (0,2) -- (3,4);
    \draw[fill] (2,2) circle (.05cm) node[right] {$5$};
    \draw (2,2) -- (1,4);
    \draw (2,2) -- (3,4);

    \draw[fill] (-3,4) circle (.05cm) node[right] {$4$};
    \draw (-3,4) -- (-2,6);
    \draw (-3,4) -- (0,6);
    \draw[fill] (-1,4) circle (.05cm) node[right] {$6$};
    \draw (-1,4) -- (-2,6);
    \draw (-1,4) -- (2,6);
    \draw[fill] (1,4) circle (.05cm) node[right] {$10$};
    \draw (1,4) -- (0,6);
    \draw (1,4) -- (2,6);
    \draw[fill] (3,4) circle (.05cm) node[right] {$15$};
    \draw (3,4) -- (2,6);

    \draw[fill] (-2,6) circle (.05cm) node[right] {$12$};
    \draw (-2,6) -- (0,8);
    \draw[fill] (0,6) circle (.05cm) node[right] {$20$};
    \draw (0,6) -- (0,8);
    \draw[fill] (2,6) circle (.05cm) node[right] {$30$};
    \draw (2,6) -- (0,8);

    \draw[fill] (0,8) circle (.05cm) node[right] {$60$};

    \end{tikzpicture}
    
\end{center}

Here is another example from the slides.

    \begin{center}
    \begin{tikzpicture}[scale=.75]
    \draw[fill] (-1, 0) circle (.05cm) node[right] {$a$};
    \draw[fill] (1, 0) circle (.05cm) node[right] {$b$};
    \draw[fill] (-1, 2) circle (.05cm) node[right] {$c$};
    \draw[fill] (1, 2) circle (.05cm) node[right] {$d$};
      \draw (-1,0) -- (-1,2);
      \draw (-1,0) -- (1,2);
      \draw (1,0) -- (1,2);
    \end{tikzpicture}
    \end{center}

And another
    \begin{center}
    \begin{tikzpicture}[scale=.75]
    \draw[fill] (-2, 0) circle (.05cm) node[right] {$a$};
      \draw (-2,0) -- (0,4);
    \draw[fill] (0, 0) circle (.05cm) node[right] {$b$};
      \draw (0,0) -- (-2,2);
      \draw (0,0) -- (2,2);
    \draw[fill] (2, 0) circle (.05cm) node[right] {$c$};
      \draw (2,0) -- (0,4);

    \draw[fill] (-2, 2) circle (.05cm) node[right] {$d$};
      \draw (-2,2) -- (-2,4);
    \draw[fill] (0, 2) circle (.05cm) node[right] {$e$};
      \draw (0,2) -- (-2,4);
      \draw (0,2) -- (2,4);
    \draw[fill] (2, 2) circle (.05cm) node[right] {$f$};
      \draw (2,2) -- (2,4);
    \draw[fill] (-2, 4) circle (.05cm) node[right] {$g$};
    \draw[fill] (0, 4) circle (.05cm) node[right] {$h$};
    \draw[fill] (2, 4) circle (.05cm) node[right] {$i$};

    \end{tikzpicture}
    \end{center}

    \begin{center}
    \begin{tikzpicture}[scale=.55]
    \draw[fill] (0, 0) circle (.05cm) node[right] {$a$};
      \draw (0,0) -- (-2,2);
      \draw (0,0) -- (0,2);
      \draw (0,0) -- (2,2);
    \draw[fill] (-2, 2) circle (.05cm) node[right] {$b$};
    \draw[fill] (0, 2) circle (.05cm) node[right] {$c$};
      \draw (0,2) -- (0,4);
    \draw[fill] (2, 2) circle (.05cm) node[right] {$d$};
    \draw[fill] (0, 4) circle (.05cm) node[right] {$e$};
      \draw (0,4) -- (-2,6);
      \draw (0,4) -- (0,6);
      \draw (0,4) -- (2,6);
    \draw[fill] (-2, 6) circle (.05cm) node[right] {$f$};
      \draw (-2,6) -- (-1,8);
    \draw[fill] (0, 6) circle (.05cm) node[right] {$g$};
      \draw (0,6) -- (-1,8);
      \draw (0,6) -- (1,8);
    \draw[fill] (2, 6) circle (.05cm) node[right] {$h$};
      \draw (2,6) -- (1,8);

    \draw[fill] (-1, 8) circle (.05cm) node[right] {$i$};
    \draw[fill] (1, 8) circle (.05cm) node[right] {$j$};
    \end{tikzpicture}
    \end{center}


\end{document}