I wasn't so hot at algebra but I kicked azimuth in geometry. It's a visual think / thing I guess. Which probably explains why Venn diagrams give me a kick. They say a whole lot about as laconically as it's possible to get, rather like a joke when you come to think of it.
I recommend two sites where you can feast on these set pieces: a Tumblr: Fuck Yeah Venn Diagrams; and the delightfully witty Indexed. But herewith a bunch of my favourite Venns (and a bit of earnestness toward the end). You're seeing thumbnail versions below, but click on any image to embiggen it to where you can see it properly.
Apparently, things get wild when you increase the number of sets (circles, in the above diagrams). Here's a four set construction [popup] designed by Venn himself. Notice that it uses ellipses and, so, isn't fully symmetrical. Seems only prime numbers of sets will generate that kind of symmetry. So here's a five-set example [popup]. Seven is where things came pretty much to an end until a weird and wonderful eleven set symmetrical and simple Venn diagram [popup] was created recently by Khalegh Mamakani and Frank Ruskey, a couple of Canadian profs at UBC. Now if you could draw me a 13-set symmetrical Venn, that would really separate the sheep from the goats.