I know what you're thinking: what's the difference between a Venn diagram and an Euler diagram? Good question. The following diagram should clear things up:
Just to clarify, Venn diagrams have regions for all possible combinations of groups whether there are things in those regions or not. You then use shading to indicate if things are actually found in those regions. An Euler diagram (pronounced oy-ler I found out today) on the other hand only shows a region if things exist in that region. The overlaps and non overlaps are therefore chosen according to what exists. For example, here's a Venn diagram:
So with three logical groups that describe playing cards (not all logical groups mind, I've missed out the other suit groups and every other grouping you could care to invent), in a Venn you overlap all three so every possible combination has its own region. I've then coloured in grey all the regions that have nothing in them.
The same information in an Euler diagram would look like this:
So here, it's the layout that changes according to the logic of the groups. Eg because all spades are black cards, that is to say they are a subset, that group is drawn entirely inside the other. No Red cards are black cards so those two groups are completely separate.
The diagram at the top of this post could be an Euler or a Venn, it's ambiguous. You could argue that it's both which is why a tiny simplified version of itself appears in the overlap! It's a diagram about itself. Here's a sexier recursive version:
Phew!
Any diagrams you'd like to see? Let me know in the comments.
