If it’s not possible in 2D, then maybe in three dimensions? This image is supposed to show some of the possible intersections of four sets. Not only are most people unable to think in terms of all the 64 possible combinations of six sets, the diagram does not provide much help. The image below shows a version of the Venn diagram for six sets. The simplicity and regular layout that made the two- and three-set diagram useful is nowhere to be found. The shapes of the intersections are very different, and it becomes easier to miss configurations. It’s not like people haven’t tried, though, with results ranging from pointless to downright silly.įour sets are doable, though they show the challenge as more sets are added. While Venn diagrams are great for two or even three sets, they very quickly break down when the number of sets goes beyond three. Many typical set problems are simple enough to be solved using Venn diagrams. That is not a bad thing as long as the limitations of the technique are understood. I imagine that many people think of Venn diagrams when they think of sets. There are more set operations, and they are all easily explained using Venn diagrams. The right image includes all elements that are in either A or B (but not both), i.e., dogs or black animals, but not black dogs. The left image shows A subtracted from B, i.e., black animals that are not dogs. Slightly more complex relationships are set difference and set complement. Even without being familiar with set theory, it’s still easy to understand where the criteria overlap and where they don’t. The right image shows set union: all things that are in at least one of the sets, i.e., all dogs and all black animals (including black dogs). The left image shows set intersection: all A that are also B, i.e., all dogs that are also black.
Let’s say the left set in these images contains dogs, the right one black animals.
The typical schoolbook example is of two sets and their potential interactions. It gets more interesting when more sets are involved. A set might contain all dogs: anything inside the circle is a dog, anything outside is not a dog. The inside of the circle represents elements of a particular set, the outside anything that is not in that set. The idea of the Venn diagram is simple: sets are shown as regions, typically circles. They're also an example of a technique that works very well for a particular purpose, but that entirely fails outside its well-defined scope or when the number of sets gets too large. Venn diagrams are a great way to visualize the structure of set relationships.
0 kommentar(er)
