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A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common. Usually, Venn diagrams are used to depict setintersections (denoted by an upside-down letter U). This type of diagram is used in scientific and engineering presentations, in theoretical mathematics, in computer applications, and in statistics. The drawing is an example of a Venn diagram that shows the relationship among three overlapping sets X, Y, and Z. The intersection relation is defined as the equivalent of the logic AND. An element is a member of the intersection of two sets if and only if that element is a member of both sets. Venn diagrams are generally drawn within a large rectangle that denotes the universe, the set of all elements under consideration.
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A Venn diagram consists of overlapping circles. Each circle contains all the elements of a set. Where the circles overlap shows the elements that the set have in common. Generally there are two or three circles. Anymore and the exercise becomes very complicated.. For example
We’ll call our universe “Animals”: Copyright © Elizabeth Stapel 2003-2011 All Rights Reserved Let’s say we want to classify things according to being small and furry or being a duck-bill. We draw circles to display our classifications:
Now we’ll fill in, or “populate”, the diagram. Moles, rabid skunks, platypusses, and my (dear departed) cat are all small and furry:
Swans, geese, platypusses, and Edmontosorum are all duck-bills:
Worms are small but not furry and horses are furry but not small, and neither is a duck-bill. However, they are animals; they fit inside our universe, but outside the circles.
Notice that “platypusses” is listed in both of the circles. The point of Venn diagrams is that we can show this overlap in set membership by overlapping these circles. In other words, we really should have drawn the circles overlapped, like this:
Now when we populate the Venn diagram, we’ll only have to write “platypusses” once, in the overlap:
The overlap of the two circles, containing only “platypusses”, is called the “intersection” of the two sets