Tool that draws Venn diagram from subset relation

Question

Is there a tool (LaTeX, JavaScript, Mathematica..) that allows one to draw Venn diagram automatically from subsets relations, e.g.

$$A\subset A+B$$

$$A\subset C$$

$$C\subset C+D$$

$$B \not\subset C$$

woud yield

------------------------------------------------
|                      C+D                     |
|                                              |
|  ------------------------------------------  |
|  |         A+B       |          C         |  |
|  |                   |                    |  |
|  |                   |                    |  |
|  |  ------------------------------------  |  |
|  |  |                                  |  |  |
|  |  |                A                 |  |  |
|  |  |                                  |  |  |
|  |  ------------------------------------  |  |
------------------------------------------------

(Sorry for the pitiful Ascii drawing)

Answer 1

https://tex.stackexchange.com/questions/9681/how-to-draw-venn-diagrams-especially-complements-in-latex answers it in latex but I couldn't get their answer to work in my answer, as it used tikzpicture ( seems unsupported here).