Venn Diagram
Representation of one or more sets by simple closed lines in which the elements are represented by dots.
The Venn diagram, like Carroll diagrams, is a graphic diagram used to represent logical relationships between sets and the elements in these sets.
Properties
A Venn diagram is made up of curved closed lines inside of which are gathered the elements of the sets that they represent, so that:- each element is identified by a capital letter that represents it;
- each element of the universal set is represented only once and is identified by its name (letter, number, etc.);
- each element in the universal set belongs to only one region of the diagram;
- an empty region of the diagram is cross-hatched;
- the intersections of the curved lines in the diagram are placed so that an attribute is represented by only one region; these regions are disjointed from one another.
- the representation of the subset E of a universal set U produces two regions corresponding to the attributes "belongs to" and "does not belong to" set E;
- the representation of two subsets E and F of a universal set produces four regions corresponding to the following subsets: E ∩ F, E \ F, F \ E and (E ∪ F)’;
- the representation of three subsets E, F and G of a universal set U produces 8 regions corresponding to each of the eight disjoint subsets;
- the representation of n subsets of a given universal set U produces 2n disjoint regions in a Venn diagram.
Example
Here is a Venn diagram representing the sets E = {a, b, c, d, e, f, g}, F = {c, d, e, h, i, j, k} and G = {d, e, f, g, k} in the universal set U = {a, b, c, d, e, f, g, h, i, j, k, m, n}. This diagram includes 8 disjoint regions.