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A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
A bar model used to solve an addition problem. This pictorial approach is typically used as a problem-solving tool in Singapore math. Singapore math teaches students mathematical concepts in a three-step learning process: concrete, pictorial, and abstract. [3] This learning process was based on the work of an American psychologist, Jerome Bruner.
Square of opposition. The lower case letters (a, e, i, o) are used instead of the upper case letters (A, E, I, O) here in order to be visually distinguished from the surrounding upper case letters S (Subject term) and P (Predicate term). In the Venn diagrams, black areas are empty and red areas are nonempty. White areas may or may not be empty.
The Venn diagram is constructed with a collection of simple closed curves drawn in the plane. The principle of these diagrams is that classes 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.
In commemoration of the 180th anniversary of Venn's birth, on 4 August 2014, Google replaced its normal logo on global search pages with an interactive and animated Google Doodle that incorporated the use of a Venn diagram. [24] [25] Venn Street in Clapham, London, which was the home of his grandfather, shows a Venn diagram on the street sign. [26]
In set theory the Venn diagrams tell, that there is an element in one of the red intersections. (The existential quantifications for the red intersections are combined by or. They can be combined by the exclusive or as well.) Relations like subset and implication, arranged in the same kind of matrix as above. In set theory the Venn diagrams tell,