Venn Diagram for Power Set I was wondering what the Venn Diagram for a power set might look like. For example for $\{A, B, C\}$. I'm going to go out on a limb and say it's probably not this:

However, that image is useful for picturing all the subsets, minus the empty set. Yet from my understanding it shows relationships between 3 sets, rather than within a power set.
Can anyone shed some light on this please?
 A: A well-drawn venn diagram will indeed show every combination of the sets if drawn correctly (including the emptyset... that is just the area outside of all of the circles in your image), though doing so can be difficult for beginners for four or more sets at a time (they won't simply be circles any more).
A more common way of picturing a power set however is as a boolean lattice using Hasse diagrams ordered according to the partial order induced by $\subseteq$.

The lattice corresponding to a powerset is a very well studied object, what we call a "Cube" (or hypercube if you prefer for higher dimensions).  The notation for this object can vary author to author, but usually involves something like $2^X$, reminiscent of related notations for power sets and the calculation for the number of elements in the power set and so on.  To draw a cube of dimension one higher than you are used to, draw the previous size cube... copy it... and then connect, such as is done in the picture below:

The coordinates in $n$-dimensional space can correspond to whether you do or do not include the corresponding elements in your particular element of the powerset.  The entry with coordinates all $0$ for instance corresponding to the empty set, and the coordinates all $1$ corresponding to the original set itself.
Using the language of boolean lattices, we find that the join and meet operations in lattices correspond neatly to the union and intersection operations of sets respectively.  Similarly, upsets and downsets in lattices correspond nicely to other concepts in set theory.
This is a very useful example to remember when beginning to study lattices and posets in general in greater detail.
