TITLE: What is the correct Venn diagram to represent $A\subseteq B$, $B\subseteq C$, $C\subseteq A$?
QUESTION [6 upvotes]: Give an example, and find the Venn diagram, for
$$A\subseteq B,\quad B\subseteq C, \quad C\subseteq A$$

Our solution:
We proved it to conclude that $A=B=C$.

so, the example is $A=\{1,2,3\}$, $B=\{1,2,3\}$, $C=\{1,2,3\}$
but in the Venn diagram, my friend and I disagreed. He drew three intersecting circles and put the elements in Intersection. But I think there is a mistake, I'm not sure about my solution. I drew a circle for three groups and put the elements $\{1,2,3\}$ inside.

So, the question is:

What is the right solution? Three circles or one circle?

REPLY [2 votes]: Both are Venn diagrams according to the usual definition:

sets are depicted by means of arbitrarily shaped (but bounded by simple closed curves) regions subject to a combinatorial requirement that there be exactly $2^N$ connected subregions (Cut-the-Knot)

Yours is a scaled Venn diagram:

A Venn diagram in which the area of each shape is proportional to the number of elements it contains is called an area-proportional or scaled Venn diagram. (Wikipedia)