Editing Venn diagram (section)

==Overview==
{{See also|Set (mathematics)#Basic operations}}
<div class=skin-invert-image>{{Gallery |File:Venn0001.svg|[[Intersection (set theory)|Intersection]] of two sets <math>~A \cap B</math>
|File:Venn0111.svg|[[Union (set theory)|Union]] of two sets <math>~A \cup B</math>
|File:Venn0110.svg|[[Symmetric difference]] of two sets <math>A~\triangle~B</math>
|File:Venn0010.svg|[[Complement (set theory)#Relative complement|Relative complement]] of ''A'' (left) in ''B'' (right) <math>A^c \cap B~=~B \setminus A</math>
|File:Venn1010.svg|[[Complement (set theory)#Absolute complement|Absolute complement]] of A in U  <math>A^c~=~U \setminus A</math>
}}</div>
A Venn diagram is constructed with a collection of simple closed curves drawn in a plane. According to Lewis,<ref name="Lewis1918"/> the "principle of these diagrams is that classes [or ''sets''] be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram. That is, the diagram initially leaves room for any possible relation of the classes, and the actual or given relation, can then be specified by indicating that some particular region is null or is not-null".<ref name="Lewis1918"/>{{rp|157}}

Venn diagrams normally comprise overlapping [[circle]]s. The interior of the circle symbolically represents the elements of the set, while the exterior represents elements that are not members of the set. For instance, in a two-set Venn diagram, one circle may represent the group of all [[wood]]en objects, while the other circle may represent the set of all tables. The overlapping region, or ''intersection'', would then represent the set of all wooden tables. Shapes other than circles can be employed as shown below by Venn's own higher set diagrams. Venn diagrams do not generally contain information on the relative or absolute sizes ([[cardinality]]) of sets. That is, they are [[schematic]] diagrams generally not drawn to scale.

Venn diagrams are similar to Euler diagrams. However, a Venn diagram for ''n'' component sets must contain all 2<sup>''n''</sup> hypothetically possible zones, that correspond to some combination of inclusion or exclusion in each of the component sets.<ref name="Weisstein_2020"/> Euler diagrams contain only the actually possible zones in a given context. In Venn diagrams, a shaded zone may represent an empty zone, whereas in an Euler diagram, the corresponding zone is missing from the diagram. For example, if one set represents ''dairy products'' and another ''cheeses'', the Venn diagram contains a zone for cheeses that are not dairy products. Assuming that in the context ''cheese'' means some type of dairy product, the Euler diagram has the cheese zone entirely contained within the dairy-product zone—there is no zone for (non-existent) non-dairy cheese. This means that as the number of contours increases, Euler diagrams are typically less visually complex than the equivalent Venn diagram, particularly if the number of non-empty intersections is small.<ref name="Kent_2004"/>

The difference between Euler and Venn diagrams can be seen in the following example. Take the three sets:
* <math>A = \{1,\, 2,\, 5\}</math>
* <math>B = \{1,\, 6\}</math>
* <math>C = \{4,\, 7\}</math>

The Euler and the Venn diagram of those sets are:

<gallery widths="300">
File:3-set Euler diagram.svg|Euler diagram
File:3-set Venn diagram.svg|Venn diagram
</gallery>