Help on simple Lattice diagrams [closed]

Question

I'd like some help creating some simple lattices, say to represent 3 or 4 sets and inclusion relations. I've searched, but only found very detailed results, which do interest me but I don't have the time to go that far into the matter. This may sound strange but the fact is I don't actually write latex documents at this point in my career, I just need a primitive grasp of latex to interact on Math SE.

If someone could respond with a lattice representing $C,B\subset A$, and $C,B$ not comparable with each other, it'd probably be the best way for me to learn the basics for what I need as I'd be able to look up the commands myself and go from there. Thanks.

Edit: I'm not really sure how to show my "attempt". I've basically gone through a bunch of TeX SE questions and LaTeX documentation, but I'm quite unable to discern what will even work on Math SE, and the ensuing discussions are above my level of comprehension. The best help would just be an example like I've said above.

Answer 1

Here is an example of what can be done with pstricks , and more specifically with the psmatrix environment from pst-node. The basic idea is quite simple: putting the elements of the lattice as elements of a matrix which are nodes, then connect these nodes with invisible lines. The inclusion relations are labels placed in the middle of these lines:

\documentclass[a4paper,11pt, pdf]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}%
\usepackage{lmodern, amssymb}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{pst-node}


\newpsobject{ncemptyline}{ncline}{linestyle=none}
\newcommand*\ncsubset[2]{\ncemptyline{#1}{#2}\ncput[nrot=:U]{ \subset}}
\newcommand*\ncsubsetneq[2]{\ncemptyline{#1}{#2}\ncput[nrot=:U]{\varsubsetneq}}
\newcommand*\ncvarsubsetneq[2]{\ncemptyline{#1}{#2}\ncput[nrot=:U]{\scalebox{1}[-1]{$ \varsubsetneq $}}}

\pagestyle{empty}

\begin{document}
\psset{npos = 0.45}
\[ \begin{psmatrix}[rowsep = 0.3, colsep = 0.4]
 & [name = C] C \\
[name = B] B & & [name = D] D \\
 & [name = A] A \\
   \ncvarsubsetneq{A}{B}\ncsubsetneq{A}{D}

\ncsubset{B}{C}\ncsubset{D}{C}
\end{psmatrix} \]

\end{document}