Math 2.0

Mathematical logic and foundations Concept

Venn diagram

Builds on UnionIntersectionComplement

Summary

A Venn diagram is a picture of the relations between a small number of sets. Each set is a closed curve, often a circle, inside a rectangle for the universal set. For nn sets, the curves cut the plane into 2n2^n regions, one for each combination of "in" and "out" of the sets.

Remarks

John Venn made these diagrams popular in the 1880s. The diagrams make laws such as De Morgan's laws for sets visible, but a picture is not a proof. An Euler diagram is similar, but it shows only the regions that are not empty.

Reading path

To understand this page from the ground up, read these 14 pages in order. The foundations come first.

Show the path as a graph
Element, definition, no evidence levelElementdefinitionProposition, concept, no evidence levelPropositionconceptSet, definition, no evidence levelSetdefinitionConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionPredicate, definition, no evidence levelPredicatedefinitionIntersection, definition, no evidence levelIntersectiondefinitionUnion, definition, no evidence levelUniondefinitionUniversal quantifier, definition, no evidence levelUniversal quantifierdefinitionSubset, definition, no evidence levelSubsetdefinitionUniversal set, definition, no evidence levelUniversal setdefinitionComplement, definition, no evidence levelComplementdefinitionVenn diagram, concept, no evidence levelVenn diagramconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Element definition
  2. Proposition concept
  3. Set definition
  4. Conjunction definition
  5. Disjunction definition
  6. Implication definition
  7. Predicate definition
  8. Intersection definition
  9. Union definition
  10. Universal quantifier definition
  11. Subset definition
  12. Universal set definition
  13. Complement definition
  14. Venn diagram concept

Further reading

  1. Web https://en.wikipedia.org/wiki/Venn_diagram, lead section
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Tag0KCT6DPXJK
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Kindconcept
WritingW1 stated
MSC03E20
UsesUnion, Intersection, Complement
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  • edge defines in: at least one definition (0 of 1)
  • edge instance_of in: at least two examples (0 of 2)
  • edge not_instance_of in: at least one non-example (0 of 1)
  • edge specializes both: the more general notions and the special cases (0 of 1)

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