Venn Diagram Definition
Venn diagrams were first published in John Venn's book "Symbolic Logic" in 1881. Venn diagrams are used in set theory, logic, probability, statistics and computer science. Venn Diagrams are used to represent the relationships between items.
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History
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John Venn was a logician and philosopher; he was born in 1834 and died in 1923. According to a foot note in Symbolic Logic, John Venn read over 60 logistical treatises and decided that there was a need for diagrams to explain things. "The majority of modern treaties appeal to diagrammatic aid, in order to give sensible illustration of the relations of terms propositions to one another."
Identification
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Venn diagrams consist of a rectangle representing a set of things. Inside the set are circles representing subsets that belong to the set. Seymour Lipschutz in his book "Set Theory" explains: "A set is any well-defined list, collection or class of objects. The objects in sets can be any thing: numbers people, letters rivers, etc."
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Union of Subsets
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A union B is all the items that belong to subset A and subset B. For example, if A is the subset all the black cats in the set of pets and B the subset of all blacks dogs in the set of pets, A union B would bet the sub set of all black cats and dogs in the set of pets.
Intersection
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The part of the set that belongs to both A and B is the intersection. For example, if A is the subset of all colors of cats in the set of pets and B the subset of all colors of dogs in the set of pets. The subset of only black pets would go in the middle where the circles overlap.
Example
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For example, you want to set up targeted mailings to club members. Given the set of all members in clubs, you are interested in the members that belong to three of those clubs, the sports fishermen, the sewing club and the hiking club. You want to know who belongs to all three clubs, and the total members in each club. You are given list with the names of members and which clubs they belong to. By plugging the numbers into a Venn diagram, it can be worked out who belongs to all three clubs and the totals for each club.
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References
- Photo Credit Mary Anne Thygesen
