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1815:. Joaquin and Boyles, on the other hand, proposed supplemental rules for the standard Venn diagram, in order to account for certain problem cases. For instance, regarding the issue of representing singular statements, they suggest to consider the Venn diagram circle as a representation of a set of things, and use
1460:
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can fly—for example, parrots—are then in both sets, so they correspond to points in the region where the blue and orange circles overlap. This overlapping region would only contain those elements (in this example, creatures) that are members of both the orange set (two-legged creatures) and the blue
1083:
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
1039:
A Venn diagram is constructed with a collection of simple closed curves drawn in a plane. According to Lewis, 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
561:
Humans and penguins are bipedal, and so are in the orange circle, but since they cannot fly, they appear in the left part of the orange circle, where it does not overlap with the blue circle. Mosquitoes can fly, but have six, not two, legs, so the point for mosquitoes is in the part of the blue
552:
This example involves two sets of creatures, represented here as colored circles. The orange circle represents all types of creatures that have two legs. The blue circle represents creatures that can fly. Each separate type of creature can be imagined as a point somewhere in the diagram. Living
1070:
component sets must contain all 2 hypothetically possible zones, that correspond to some combination of inclusion or exclusion in each of the component sets. Euler diagrams contain only the actually possible zones in a given context. In Venn diagrams, a shaded zone may represent an empty zone,
1804:
521:, which do not necessarily show all relations. Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics, and computer science.
1627:
constructed a series of Venn diagrams for higher numbers of sets by segmenting the surface of a sphere, which became known as
Edwards–Venn diagrams. For example, three sets can be easily represented by taking three hemispheres of the sphere at right angles
653:
Venn did not use the term "Venn diagram" and referred to the concept as "Eulerian
Circles". He became acquainted with Euler diagrams in 1862 and wrote that Venn diagrams did not occur to him "till much later", while attempting to adapt Euler diagrams to
1640: = 0). A fourth set can be added to the representation, by taking a curve similar to the seam on a tennis ball, which winds up and down around the equator, and so on. The resulting sets can then be projected back to a plane, to give
1047:. 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
1055:, 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 (
575:, where A is the orange circle and B the blue. The union in this case contains all living creatures that either are two-legged or can fly (or both). The region included in both A and B, where the two sets overlap, is called the
1040:
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".
1389:
For higher numbers of sets, some loss of symmetry in the diagrams is unavoidable. Venn was keen to find "symmetrical figures ... elegant in themselves," that represented higher numbers of sets, and he devised an
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as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled
1253:
Venn diagrams typically represent two or three sets, but there are forms that allow for higher numbers. Shown below, four intersecting spheres form the highest order Venn diagram that has the symmetry of a
1477:
a Venn diagram for four sets as it has only 14 regions as opposed to 2 = 16 regions (including the white region); there is no region where only the yellow and blue, or only the red and green circles meet.
1895:, etc., in the sense that each region of Venn diagram corresponds to one row of the truth table. This type is also known as Johnston diagram. Another way of representing sets is with John F. Randolph's
742:= 11 and in 2003, Griggs, Killian, and Savage showed that symmetric Venn diagrams exist for all other primes. These combined results show that rotationally symmetric Venn diagrams exist, if and only if
661:
Venn viewed his diagrams as a pedagogical tool, analogous to verification of physical concepts through experiment. As an example of their applications, he noted that a three-set diagram could show the
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circle that does not overlap with the orange one. Creatures that are neither two-legged nor able to fly (for example, whales and spiders) would all be represented by points outside both circles.
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and Mark Weston, predates Venn but are "rightly associated" with him as he "comprehensively surveyed and formalized their usage, and was the first to generalize them".
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1823:. So, for example, to represent the statement "a is F" in this retooled Venn diagram, a small letter "a" may be placed inside the circle that represents the set F.
638:(1646–1716) produced similar diagrams in the 17th century (though much of this work was unpublished), as did Johann Christian Lange in a work from 1712 describing
658:. In the opening sentence of his 1880 article Venn wrote that Euler diagrams were the only diagrammatic representation of logic to gain "any general acceptance".
1945:– A stereographic projection of a regular octahedron makes a three-set Venn diagram, as three orthogonal great circles, each dividing space into two halves.
859:
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and set theory to treat categorical statements as statements about sets. Additionally, they propose to treat singular statements as statements about
646:, which are similar to Venn diagrams but don't necessarily contain all possible unions and intersections, were first made prominent by mathematician
1555:
517:
In Venn diagrams, the curves are overlapped in every possible way, showing all possible relations between the sets. They are thus a special case of
773:
695:(Lewis Carroll) includes "Venn's Method of Diagrams" as well as "Euler's Method of Diagrams" in an "Appendix, Addressed to Teachers" of his book
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number of sets, where each successive curve that delimits a set interleaves with previous curves, starting with the three-circle diagram.
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2227:
420:. A Venn diagram uses simple closed curves drawn on a plane to represent sets. Very often, these curves are circles or ellipses.
360:
1799:{\displaystyle y_{i}={\frac {\sin \left(2^{i}x\right)}{2^{i}}}{\text{ where }}0\leq i\leq n-1{\text{ and }}i\in \mathbb {N} .}
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482:. This lends itself to intuitive visualizations; for example, the set of all elements that are members of both sets
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whereas in an Euler diagram, the corresponding zone is missing from the diagram. For example, if one set represents
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movement in the 1960s. Since then, they have also been adopted in the curriculum of other fields such as reading.
524:
A Venn diagram in which the area of each shape is proportional to the number of elements it contains is called an
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2414:(NB. Has a detailed history of the evolution of logic diagrams including but not limited to the Venn diagram.)
611:
in a paper entitled "On the
Diagrammatic and Mechanical Representation of Propositions and Reasonings" in the
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Diagrams of overlapping circles representing unions and intersections were introduced by
Catalan philosopher
17:
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437:
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In Venn's article, however, he suggests that the diagrammatic idea predates Euler, and is attributable to
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The difference between Euler and Venn diagrams can be seen in the following example. Take the three sets:
990:
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1079:, the Venn diagram contains a zone for cheeses that are not dairy products. Assuming that in the context
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Venn diagrams and Euler diagrams were incorporated as part of instruction in set theory, as part of the
5447:
4455:
4045:
3439:
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diagrams with increasing numbers of teeth—as shown here. These diagrams were devised while designing a
634:(c. 1232–1315/1316) in the 13th century, who used them to illustrate combinations of basic principles.
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VBVenn, a free open source program for calculating and graphing quantitative two-circle Venn diagrams
2800:
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2189:"On the employment of geometrical diagrams for the sensible representations of logical propositions"
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possible logical relations between a finite collection of different sets. These diagrams depict
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objects, while the other circle may represent the set of all tables. The overlapping region, or
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2300:
2103:"The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics"
822:
692:
567:
261:
150:
90:
67:
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1661:
1601:
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and can be visually represented. The 16 intersections correspond to the vertices of a
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2312:
2136:"I. On the Diagrammatic and Mechanical Representation of Propositions and Reasonings"
2056:
1908:
1816:
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226:
125:
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3328:
3290:
2856:(NB. The book comes with a 3-page foldout of a seven-bit cylindrical Venn diagram.)
2680:
2489:
2292:
2152:
1989:
Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie
1928:
1668:
with increasing numbers of sides. They are also two-dimensional representations of
593:
417:
145:
75:
49:
2527:
2082:"On the Diagrammatic and Mechanical Representation of Propositions and Reasonings"
544:
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1996:
639:
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45:
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3071:
2717:
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2330:
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2144:
The London, Edinburgh, and Dublin
Philosophical Magazine and Journal of Science
1991:(Saint Petersburg, Russia: l'Academie Impériale des Sciences, 1768), volume 2,
1820:
1418:
to compute, the digit 1 means in the set, and the digit 0 means not in the set)
647:
432:
236:
41:
2558:
2156:
1084:
Venn diagram, particularly if the number of non-empty intersections is small.
27:
Diagram that shows all possible logical relations between a collection of sets
5548:
5428:
5230:
5144:
5139:
4658:
4336:
3843:
3628:
3618:
3588:
3573:
3243:
2876:
2823:
1963:
1645:
1470:
1350:
1310:
1280:
738:
is five or seven. In 2002, Peter
Hamburger found symmetric Venn diagrams for
655:
643:
597:
518:
109:
5398:
1380:
1372:
1367:
1362:
1357:
1342:
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3603:
3088:
2991:
2921:
2902:
2519:
2515:
2251:
1936:
1932:
731:
699:(4th edition published in 1896). The term "Venn diagram" was later used by
624:
620:
246:
130:
5514:
5403:
5038:
4668:
4548:
3727:
3717:
3664:
3348:
3268:
3253:
3133:
3078:
2841:
2667:"Teaching Syllogistic Logic via a Retooled Venn Diagrammatical Technique"
1840:
1066:
Venn diagrams are similar to Euler diagrams. However, a Venn diagram for
1056:
631:
616:
413:
401:
256:
97:
85:
5534:
3001:
32:
5383:
5154:
4810:
3598:
3453:
3424:
3230:
3011:
2523:
2501:
2304:
1968:
409:
397:
114:
60:
2281:(May 1969). "A Note on The Historical Development of Logic Diagrams".
478:, while points outside the boundary represent elements not in the set
5186:
5149:
5100:
4998:
4750:
4653:
3706:
3623:
3583:
3547:
3483:
3295:
3285:
3258:
3021:
2351:
2184:
2131:
1958:
1896:
1669:
1415:
1259:
1060:
662:
608:
393:
5439:
2493:
2296:
1497:. Labels have been simplified for greater readability; for example,
396:(1834–1923) in the 1880s. The diagrams are used to teach elementary
4735:
4533:
3981:
3686:
3280:
750:
241:
2934:
1811:(also known as Lewis Carroll) devised a five-set diagram known as
4331:
3123:
1665:
1395:
1263:
1255:
506:", is represented visually by the area of overlap of the regions
385:
2427:
Verburgt, Lukas M. (April 2023). "The Venn Behind the
Diagram".
5211:
5033:
1398:(see below). He also gave a construction for Venn diagrams for
1044:
2751:. Springer Undergraduate Mathematics Series. Berlin, Germany:
2665:
Joaquin, Jeremiah Joven; Boyles, Robert James M. (June 2017).
1489:
Five-set Venn diagram using congruent ellipses in a five-fold
734:. He also showed that such symmetric Venn diagrams exist when
445:, Chapter V "Diagrammatic Representation", published in 1881.
5083:
4843:
4779:
3875:
3221:
3066:
3017:
DeepVenn, a tool for creating area-proportional Venn
Diagrams
3012:
InteractiVenn, a web-based tool for visualizing Venn diagrams
405:
37:
3016:
2607:. Reasoning with Diagrams project, University of Kent. 2004
1831:
1683:
1048:
710:
In the 20th century, Venn diagrams were further developed.
2899:
Morphs, Mallards, and
Montages: Computer-Aided Imagination
2478:(April 1963). "Venn diagrams for more than four classes".
2926:"A New Rose: The First Simple Symmetric 11-Venn Diagram"
1248:
548:
Sets of creatures with two legs, and creatures that fly
423:
Similar ideas had been proposed before Venn such as by
2784:
2329:(1903) . "De Formae Logicae per linearum ductus". In
1875:
1849:
1692:
1183:
1143:
1096:
993:
928:
874:
831:
788:
2605:"Euler Diagrams 2004: Brighton, UK: September 22–23"
2555:"Strategies for Reading Comprehension Venn Diagrams"
565:
The combined region of the two sets is called their
2871:(reprint of 1st ed.). Mineola, New York, USA:
619:by diagrams. The use of these types of diagrams in
2836:Watkinson, John (1990). "4.10. Hamming distance".
2194:Proceedings of the Cambridge Philosophical Society
1887:
1861:
1798:
1219:The Euler and the Venn diagram of those sets are:
1208:
1168:
1128:
1024:
965:
892:
846:
803:
2636:Cogwheels of the Mind: The Story of Venn Diagrams
2514:
5546:
2797:Eighteenth Annual Iranian Mathematics Conference
400:, and to illustrate simple set relationships in
2625:
2623:
2621:
2528:"The Search for Simple Symmetric Venn Diagrams"
441:) in 1768. The idea was popularised by Venn in
2919:
2572:
2468:
2422:
2420:
2210:
2208:
388:style that shows the logical relation between
5455:
4795:
3037:
2821:(1989-01-07). "Venn diagrams for many sets".
2702:
2664:
2433:Institute of Mathematics and its Applications
613:Philosophical Magazine and Journal of Science
361:
2734:
2658:
2618:
2446:
2444:
2442:
2378:
2319:
2273:
2271:
2250:
2246:
2244:
2179:
2177:
2126:
2124:
1561:Six-set Venn diagram made of only triangles
1203:
1190:
1163:
1150:
1123:
1103:
1043:Venn diagrams normally comprise overlapping
2988:Lewis Carroll's Logic Game – Venn vs. Euler
2508:
2417:
2346:
2344:
2205:
1999:or Johann Christian Lange (in Lange's book
5462:
5448:
4802:
4788:
3229:
3044:
3030:
2997:Six sets Venn diagrams made from triangles
2799:. Tehran and Isfahan, Iran. Archived from
2547:
2335:Opuscules et fragmentes inedits de Leibniz
966:{\displaystyle A^{c}\cap B~=~B\setminus A}
714:showed, in 1963, that the existence of an
368:
354:
2933:
2844:. pp. 94–99, foldout in backsleeve.
2835:
2597:
2474:
2439:
2384:
2268:
2241:
2174:
2121:
1789:
1199:
1159:
1119:
1112:
763:Set (mathematics) § Basic operations
607:Venn diagrams were introduced in 1880 by
2893:
2708:
2426:
2341:
2214:
2073:
2017:
1830:
1569:
615:, about the different ways to represent
592:
543:
31:
2859:
2817:
2740:
2629:
2325:
2261:The Electronic Journal of Combinatorics
2228:The Mathematical Association of America
1664:, which were based around intersecting
1414:Venn's construction for four sets (use
1063:diagrams generally not drawn to scale.
14:
5547:
3051:
2788:; Rezaie, M.; Vatan, F. (March 1987).
2748:Elements of logic via numbers and sets
2714:Discrete and combinatorial mathematics
1454:Venn's four-set diagram using ellipses
5469:
5443:
4783:
3025:
2578:
2450:
2277:
602:Gonville and Caius College, Cambridge
5505:Propositional directed acyclic graph
2869:Another Fine Math You've Got Me Into
2350:
2183:
2130:
2051:
2049:
1981:
1686:curves with the series of equations
1249:Extensions to higher numbers of sets
1025:{\displaystyle A^{c}~=~U\setminus A}
3002:Interactive seven sets Venn diagram
2385:Mac Queen, Gailand (October 1967).
1826:
36:Venn diagram showing the uppercase
24:
2865:"Chapter 4. Cogwheels of the Mind"
2777:
881:
25:
5581:
2963:
2819:Edwards, Anthony William Fairbank
2631:Edwards, Anthony William Fairbank
2095:
2046:
1651:
1430:Venn's construction for five sets
1016:
957:
5555:Graphical concepts in set theory
5533:
4833:
4763:
2790:"Generalization of Venn Diagram"
2166:from the original on 2017-05-16.
2079:
1625:Anthony William Fairbank Edwards
1612:
1600:
1588:
1576:
1554:
1482:
1459:
1447:
1442:Venn's construction for six sets
1435:
1423:
1407:
1379:
1371:
1366:
1361:
1356:
1349:
1341:
1336:
1331:
1326:
1321:
1316:
1309:
1301:
1296:
1291:
1286:
1279:
1272:
1236:
1224:
977:
904:
858:
815:
772:
74:
5565:Statistical charts and diagrams
2950:from the original on 2017-05-01
2691:from the original on 2018-11-21
1129:{\displaystyle A=\{1,\,2,\,5\}}
4809:
2641:Johns Hopkins University Press
2462:University of California Press
893:{\displaystyle A~\triangle ~B}
498:and read "the intersection of
474:represent elements of the set
453:A Venn diagram, also called a
141:Collectively exhaustive events
13:
1:
4724:History of mathematical logic
2481:American Mathematical Monthly
2337:(in Latin). pp. 292–321.
2254:; Weston, Mark (2005-06-18).
2010:
1835:Venn diagram as a truth table
1059:) of sets. That is, they are
553:creatures that have two legs
4649:Primitive recursive function
2838:Coding for Digital Recording
2639:. Baltimore, Maryland, USA:
2431:. Vol. 59, no. 2.
1839:Venn diagrams correspond to
600:window with Venn diagram in
438:Letters to a German Princess
7:
5525:Method of analytic tableaux
5510:Sentential decision diagram
2976:Encyclopedia of Mathematics
2256:"A Survey of Venn Diagrams"
1931:(and as further derivation
1902:
1209:{\displaystyle C=\{4,\,7\}}
1169:{\displaystyle B=\{1,\,6\}}
756:
642:'s contributions to logic.
10:
5586:
5300:von Neumann–Bernays–Gödel
3713:Schröder–Bernstein theorem
3440:Monadic predicate calculus
3099:Foundations of mathematics
2741:Johnson, David L. (2001).
2685:10.5840/teachphil201771767
2457:A Survey of Symbolic Logic
2327:Leibniz, Gottfried Wilhelm
1656:Edwards–Venn diagrams are
1648:window in memory of Venn.
1563:(interactive version)
760:
705:A Survey of Symbolic Logic
588:
539:
448:
5531:
5475:
5364:
5327:
5239:
5129:
5101:One-to-one correspondence
5017:
4958:
4842:
4831:
4817:
4759:
4746:Philosophy of mathematics
4695:Automated theorem proving
4677:
4572:
4404:
4297:
4149:
3866:
3842:
3820:Von Neumann–Bernays–Gödel
3765:
3659:
3563:
3461:
3452:
3379:
3314:
3220:
3142:
3059:
2157:10.1080/14786448008626877
2001:Nucleus Logicae Weisianae
636:Gottfried Wilhelm Leibniz
429:Nucleus Logicoe Wiesianoe
2897:(2004). "Venn and Now".
2873:Dover Publications, Inc.
2786:Mahmoodian, Ebadollah S.
2284:The Mathematical Gazette
2057:"Sets and Venn Diagrams"
1974:
1809:Charles Lutwidge Dodgson
1676:Henry John Stephen Smith
1658:topologically equivalent
1491:rotationally symmetrical
847:{\displaystyle ~A\cup B}
804:{\displaystyle ~A\cap B}
558:set (flying creatures).
311:Law of total probability
306:Conditional independence
195:Exponential distribution
180:Probability distribution
5500:Binary decision diagram
4396:Self-verifying theories
4217:Tarski's axiomatization
3168:Tarski's undefinability
3163:incompleteness theorems
2476:Henderson, David Wilson
1660:to diagrams devised by
1493:arrangement devised by
1394:four-set diagram using
581:of A and B, denoted by
290:Conditional probability
5059:Constructible universe
4879:Constructibility (V=L)
4770:Mathematics portal
4381:Proof of impossibility
4029:propositional variable
3339:Propositional calculus
2901:. Wellesley, MA, USA:
2452:Lewis, Clarence Irving
2025:"Intersection of Sets"
1913:Charles Sanders Peirce
1889:
1888:{\displaystyle x\in B}
1863:
1862:{\displaystyle x\in A}
1836:
1800:
1210:
1170:
1130:
1026:
967:
894:
848:
805:
712:David Wilson Henderson
650:in the 18th century.
604:
549:
232:Continuous or discrete
185:Bernoulli distribution
53:
5282:Principia Mathematica
5116:Transfinite induction
4975:(i.e. set difference)
4639:Kolmogorov complexity
4592:Computably enumerable
4492:Model complete theory
4284:Principia Mathematica
3344:Propositional formula
3173:Banach–Tarski paradox
2840:. Stoneham, MA, USA:
2585:mathworld.wolfram.com
2215:Sandifer, Ed (2003).
1949:Stanhope Demonstrator
1890:
1864:
1843:for the propositions
1834:
1801:
1570:Edwards–Venn diagrams
1211:
1171:
1131:
1027:
968:
895:
849:
806:
703:in 1918, in his book
701:Clarence Irving Lewis
596:
547:
190:Binomial distribution
35:
5485:Square of opposition
5356:Burali-Forti paradox
5111:Set-builder notation
5064:Continuum hypothesis
5004:Symmetric difference
4587:Church–Turing thesis
4574:Computability theory
3783:continuum hypothesis
3301:Square of opposition
3159:Gödel's completeness
2905:. pp. 161–184.
2108:Taylor & Francis
1943:Spherical octahedron
1873:
1847:
1690:
1682:-set diagrams using
1181:
1141:
1094:
991:
926:
872:
866:Symmetric difference
829:
786:
316:Law of large numbers
285:Marginal probability
210:Poisson distribution
59:Part of a series on
5317:Tarski–Grothendieck
4741:Mathematical object
4632:P versus NP problem
4597:Computable function
4391:Reverse mathematics
4317:Logical consequence
4194:primitive recursive
4189:elementary function
3962:Free/bound variable
3815:Tarski–Grothendieck
3334:Logical connectives
3264:Logical equivalence
3114:Logical consequence
2944:2012arXiv1207.6452M
2920:Mamakani, Khalegh;
2879:). pp. 51–64.
2672:Teaching Philosophy
2579:Weisstein, Eric W.
2396:McMaster University
1954:Three circles model
1924:Information diagram
1919:Logical connectives
1636: = 0 and
1262:(or the cells of a
985:Absolute complement
912:Relative complement
746:is a prime number.
724:rotational symmetry
718:-Venn diagram with
275:Complementary event
217:Probability measure
205:Pareto distribution
200:Normal distribution
48:(upper right), and
4906:Limitation of size
4539:Transfer principle
4502:Semantics of logic
4487:Categorical theory
4463:Non-standard model
3977:Logical connective
3104:Information theory
3053:Mathematical logic
2710:Grimaldi, Ralph P.
2536:Notices of the AMS
2279:Baron, Margaret E.
2217:"How Euler Did It"
2061:www.mathsisfun.com
1885:
1859:
1837:
1796:
1206:
1166:
1126:
1022:
963:
890:
844:
801:
693:Charles L. Dodgson
605:
550:
326:Boole's inequality
262:Stochastic process
151:Mutual exclusivity
68:Probability theory
54:
52:(bottom) alphabets
5542:
5541:
5470:Diagrams in logic
5437:
5436:
5346:Russell's paradox
5295:Zermelo–Fraenkel
5196:Dedekind-infinite
5069:Diagonal argument
4968:Cartesian product
4825:Set (mathematics)
4777:
4776:
4709:Abstract category
4512:Theories of truth
4322:Rule of inference
4312:Natural deduction
4293:
4292:
3838:
3837:
3543:Cartesian product
3448:
3447:
3354:Many-valued logic
3329:Boolean functions
3212:Russell's paradox
3187:diagonal argument
3084:First-order logic
2886:978-0-486-43181-9
2851:978-0-240-51293-8
2766:978-3-540-76123-5
2727:978-0-201-72634-3
2650:978-0-8018-7434-5
2526:(December 2006).
2435:. pp. 53–55.
2429:Mathematics Today
2388:The Logic Diagram
1909:Existential graph
1817:first-order logic
1780:
1754:
1753: where
1749:
1387:
1386:
1266:, respectively).
1012:
1006:
953:
947:
886:
880:
834:
791:
526:area-proportional
392:, popularized by
384:is a widely used
378:
377:
280:Joint probability
227:Bernoulli process
126:Probability space
16:(Redirected from
5577:
5570:Logical diagrams
5537:
5520:Sequent calculus
5464:
5457:
5450:
5441:
5440:
5419:Bertrand Russell
5409:John von Neumann
5394:Abraham Fraenkel
5389:Richard Dedekind
5351:Suslin's problem
5262:Cantor's theorem
4979:De Morgan's laws
4837:
4804:
4797:
4790:
4781:
4780:
4768:
4767:
4719:History of logic
4714:Category of sets
4607:Decision problem
4386:Ordinal analysis
4327:Sequent calculus
4225:Boolean algebras
4165:
4164:
4139:
4110:logical/constant
3864:
3863:
3850:
3773:Zermelo–Fraenkel
3524:Set operations:
3459:
3458:
3396:
3227:
3226:
3207:Löwenheim–Skolem
3094:Formal semantics
3046:
3039:
3032:
3023:
3022:
2984:
2958:
2956:
2955:
2937:
2928:. p. 6452.
2916:
2895:Glassner, Andrew
2890:
2855:
2832:
2814:
2812:
2811:
2805:
2794:
2771:
2770:
2738:
2732:
2731:
2706:
2700:
2699:
2697:
2696:
2662:
2656:
2654:
2627:
2616:
2615:
2613:
2612:
2601:
2595:
2594:
2592:
2591:
2576:
2570:
2569:
2567:
2566:
2557:. Archived from
2551:
2545:
2544:
2543:(11): 1304–1311.
2532:
2520:Savage, Carla D.
2512:
2506:
2505:
2472:
2466:
2465:
2448:
2437:
2436:
2424:
2415:
2413:
2411:
2410:
2404:
2398:. Archived from
2393:
2382:
2376:
2375:
2373:
2372:
2348:
2339:
2338:
2323:
2317:
2316:
2291:(384): 113–125.
2275:
2266:
2265:
2248:
2239:
2238:
2236:
2235:
2221:
2212:
2203:
2202:
2181:
2172:
2167:
2165:
2140:
2128:
2119:
2118:
2116:
2115:
2099:
2093:
2092:
2089:Penn Engineering
2086:
2077:
2071:
2070:
2068:
2067:
2053:
2044:
2043:
2041:
2040:
2031:. Archived from
2021:
2004:
1985:
1929:Marquand diagram
1894:
1892:
1891:
1886:
1868:
1866:
1865:
1860:
1827:Related concepts
1813:Carroll's square
1805:
1803:
1802:
1797:
1792:
1781:
1778:
1755:
1752:
1750:
1748:
1747:
1738:
1737:
1733:
1729:
1728:
1707:
1702:
1701:
1678:devised similar
1632: = 0,
1616:
1604:
1592:
1580:
1558:
1548:
1522:
1486:
1463:
1451:
1439:
1427:
1411:
1383:
1375:
1370:
1365:
1360:
1353:
1345:
1340:
1335:
1330:
1325:
1320:
1313:
1305:
1300:
1295:
1290:
1283:
1276:
1269:
1268:
1240:
1228:
1215:
1213:
1212:
1207:
1175:
1173:
1172:
1167:
1135:
1133:
1132:
1127:
1031:
1029:
1028:
1023:
1010:
1004:
1003:
1002:
981:
972:
970:
969:
964:
951:
945:
938:
937:
908:
899:
897:
896:
891:
884:
878:
862:
853:
851:
850:
845:
832:
819:
810:
808:
807:
802:
789:
776:
584:
574:
418:computer science
370:
363:
356:
146:Elementary event
78:
56:
55:
50:Russian Cyrillic
21:
5585:
5584:
5580:
5579:
5578:
5576:
5575:
5574:
5545:
5544:
5543:
5538:
5529:
5490:Porphyrian tree
5471:
5468:
5438:
5433:
5360:
5339:
5323:
5288:New Foundations
5235:
5125:
5044:Cardinal number
5027:
5013:
4954:
4838:
4829:
4813:
4808:
4778:
4773:
4762:
4755:
4700:Category theory
4690:Algebraic logic
4673:
4644:Lambda calculus
4582:Church encoding
4568:
4544:Truth predicate
4400:
4366:Complete theory
4289:
4158:
4154:
4150:
4145:
4137:
3857: and
3853:
3848:
3834:
3810:New Foundations
3778:axiom of choice
3761:
3723:Gödel numbering
3663: and
3655:
3559:
3444:
3394:
3375:
3324:Boolean algebra
3310:
3274:Equiconsistency
3239:Classical logic
3216:
3197:Halting problem
3185: and
3161: and
3149: and
3148:
3143:Theorems (
3138:
3055:
3050:
2969:
2966:
2961:
2953:
2951:
2913:
2887:
2852:
2809:
2807:
2803:
2792:
2780:
2778:Further reading
2775:
2774:
2767:
2753:Springer-Verlag
2739:
2735:
2728:
2720:. p. 143.
2707:
2703:
2694:
2692:
2663:
2659:
2651:
2628:
2619:
2610:
2608:
2603:
2602:
2598:
2589:
2587:
2577:
2573:
2564:
2562:
2553:
2552:
2548:
2530:
2513:
2509:
2494:10.2307/2311865
2473:
2469:
2449:
2440:
2425:
2418:
2408:
2406:
2402:
2391:
2383:
2379:
2370:
2368:
2349:
2342:
2331:Couturat, Louis
2324:
2320:
2297:10.2307/3614533
2276:
2269:
2249:
2242:
2233:
2231:
2219:
2213:
2206:
2182:
2175:
2163:
2138:
2129:
2122:
2113:
2111:
2101:
2100:
2096:
2084:
2078:
2074:
2065:
2063:
2055:
2054:
2047:
2038:
2036:
2029:web.mnstate.edu
2023:
2022:
2018:
2013:
2008:
2007:
1997:Christian Weise
1986:
1982:
1977:
1905:
1874:
1871:
1870:
1848:
1845:
1844:
1829:
1788:
1779: and
1777:
1751:
1743:
1739:
1724:
1720:
1719:
1715:
1708:
1706:
1697:
1693:
1691:
1688:
1687:
1662:Branko Grünbaum
1654:
1620:
1617:
1608:
1605:
1596:
1593:
1584:
1581:
1572:
1565:
1559:
1550:
1528:
1502:
1495:Branko Grünbaum
1487:
1478:
1464:
1455:
1452:
1443:
1440:
1431:
1428:
1419:
1412:
1354:
1314:
1284:
1251:
1244:
1241:
1232:
1229:
1182:
1179:
1178:
1142:
1139:
1138:
1095:
1092:
1091:
1037:
1036:
1035:
1032:
998:
994:
992:
989:
988:
982:
973:
933:
929:
927:
924:
923:
909:
900:
873:
870:
869:
863:
854:
830:
827:
826:
820:
811:
787:
784:
783:
777:
765:
759:
640:Christian Weise
623:, according to
591:
582:
572:
542:
451:
425:Christian Weise
374:
222:Random variable
173:Bernoulli trial
28:
23:
22:
15:
12:
11:
5:
5583:
5573:
5572:
5567:
5562:
5557:
5540:
5539:
5532:
5530:
5528:
5527:
5522:
5517:
5512:
5507:
5502:
5497:
5492:
5487:
5482:
5476:
5473:
5472:
5467:
5466:
5459:
5452:
5444:
5435:
5434:
5432:
5431:
5426:
5424:Thoralf Skolem
5421:
5416:
5411:
5406:
5401:
5396:
5391:
5386:
5381:
5376:
5370:
5368:
5362:
5361:
5359:
5358:
5353:
5348:
5342:
5340:
5338:
5337:
5334:
5328:
5325:
5324:
5322:
5321:
5320:
5319:
5314:
5309:
5308:
5307:
5292:
5291:
5290:
5278:
5277:
5276:
5265:
5264:
5259:
5254:
5249:
5243:
5241:
5237:
5236:
5234:
5233:
5228:
5223:
5218:
5209:
5204:
5199:
5189:
5184:
5183:
5182:
5177:
5172:
5162:
5152:
5147:
5142:
5136:
5134:
5127:
5126:
5124:
5123:
5118:
5113:
5108:
5106:Ordinal number
5103:
5098:
5093:
5088:
5087:
5086:
5081:
5071:
5066:
5061:
5056:
5051:
5041:
5036:
5030:
5028:
5026:
5025:
5022:
5018:
5015:
5014:
5012:
5011:
5006:
5001:
4996:
4991:
4986:
4984:Disjoint union
4981:
4976:
4970:
4964:
4962:
4956:
4955:
4953:
4952:
4951:
4950:
4945:
4934:
4933:
4931:Martin's axiom
4928:
4923:
4918:
4913:
4908:
4903:
4898:
4896:Extensionality
4893:
4892:
4891:
4881:
4876:
4875:
4874:
4869:
4864:
4854:
4848:
4846:
4840:
4839:
4832:
4830:
4828:
4827:
4821:
4819:
4815:
4814:
4807:
4806:
4799:
4792:
4784:
4775:
4774:
4760:
4757:
4756:
4754:
4753:
4748:
4743:
4738:
4733:
4732:
4731:
4721:
4716:
4711:
4702:
4697:
4692:
4687:
4685:Abstract logic
4681:
4679:
4675:
4674:
4672:
4671:
4666:
4664:Turing machine
4661:
4656:
4651:
4646:
4641:
4636:
4635:
4634:
4629:
4624:
4619:
4614:
4604:
4602:Computable set
4599:
4594:
4589:
4584:
4578:
4576:
4570:
4569:
4567:
4566:
4561:
4556:
4551:
4546:
4541:
4536:
4531:
4530:
4529:
4524:
4519:
4509:
4504:
4499:
4497:Satisfiability
4494:
4489:
4484:
4483:
4482:
4472:
4471:
4470:
4460:
4459:
4458:
4453:
4448:
4443:
4438:
4428:
4427:
4426:
4421:
4414:Interpretation
4410:
4408:
4402:
4401:
4399:
4398:
4393:
4388:
4383:
4378:
4368:
4363:
4362:
4361:
4360:
4359:
4349:
4344:
4334:
4329:
4324:
4319:
4314:
4309:
4303:
4301:
4295:
4294:
4291:
4290:
4288:
4287:
4279:
4278:
4277:
4276:
4271:
4270:
4269:
4264:
4259:
4239:
4238:
4237:
4235:minimal axioms
4232:
4221:
4220:
4219:
4208:
4207:
4206:
4201:
4196:
4191:
4186:
4181:
4168:
4166:
4147:
4146:
4144:
4143:
4142:
4141:
4129:
4124:
4123:
4122:
4117:
4112:
4107:
4097:
4092:
4087:
4082:
4081:
4080:
4075:
4065:
4064:
4063:
4058:
4053:
4048:
4038:
4033:
4032:
4031:
4026:
4021:
4011:
4010:
4009:
4004:
3999:
3994:
3989:
3984:
3974:
3969:
3964:
3959:
3958:
3957:
3952:
3947:
3942:
3932:
3927:
3925:Formation rule
3922:
3917:
3916:
3915:
3910:
3900:
3899:
3898:
3888:
3883:
3878:
3873:
3867:
3861:
3844:Formal systems
3840:
3839:
3836:
3835:
3833:
3832:
3827:
3822:
3817:
3812:
3807:
3802:
3797:
3792:
3787:
3786:
3785:
3780:
3769:
3767:
3763:
3762:
3760:
3759:
3758:
3757:
3747:
3742:
3741:
3740:
3733:Large cardinal
3730:
3725:
3720:
3715:
3710:
3696:
3695:
3694:
3689:
3684:
3669:
3667:
3657:
3656:
3654:
3653:
3652:
3651:
3646:
3641:
3631:
3626:
3621:
3616:
3611:
3606:
3601:
3596:
3591:
3586:
3581:
3576:
3570:
3568:
3561:
3560:
3558:
3557:
3556:
3555:
3550:
3545:
3540:
3535:
3530:
3522:
3521:
3520:
3515:
3505:
3500:
3498:Extensionality
3495:
3493:Ordinal number
3490:
3480:
3475:
3474:
3473:
3462:
3456:
3450:
3449:
3446:
3445:
3443:
3442:
3437:
3432:
3427:
3422:
3417:
3412:
3411:
3410:
3400:
3399:
3398:
3385:
3383:
3377:
3376:
3374:
3373:
3372:
3371:
3366:
3361:
3351:
3346:
3341:
3336:
3331:
3326:
3320:
3318:
3312:
3311:
3309:
3308:
3303:
3298:
3293:
3288:
3283:
3278:
3277:
3276:
3266:
3261:
3256:
3251:
3246:
3241:
3235:
3233:
3224:
3218:
3217:
3215:
3214:
3209:
3204:
3199:
3194:
3189:
3177:Cantor's
3175:
3170:
3165:
3155:
3153:
3140:
3139:
3137:
3136:
3131:
3126:
3121:
3116:
3111:
3106:
3101:
3096:
3091:
3086:
3081:
3076:
3075:
3074:
3063:
3061:
3057:
3056:
3049:
3048:
3041:
3034:
3026:
3020:
3019:
3014:
3009:
3004:
2999:
2994:
2985:
2971:"Venn diagram"
2965:
2964:External links
2962:
2960:
2959:
2924:(2012-07-27).
2917:
2912:978-1568812311
2911:
2891:
2885:
2863:(June 2003) .
2857:
2850:
2833:
2831:(1646): 51–56.
2815:
2781:
2779:
2776:
2773:
2772:
2765:
2733:
2726:
2718:Addison-Wesley
2701:
2679:(2): 161–180.
2657:
2649:
2643:. p. 65.
2617:
2596:
2581:"Venn Diagram"
2571:
2546:
2507:
2488:(4): 424–426.
2467:
2438:
2416:
2377:
2357:Symbolic logic
2340:
2318:
2267:
2240:
2204:
2173:
2120:
2094:
2072:
2045:
2015:
2014:
2012:
2009:
2006:
2005:
1979:
1978:
1976:
1973:
1972:
1971:
1966:
1961:
1956:
1951:
1946:
1940:
1926:
1921:
1916:
1904:
1901:
1884:
1881:
1878:
1858:
1855:
1852:
1828:
1825:
1821:set membership
1795:
1791:
1787:
1784:
1776:
1773:
1770:
1767:
1764:
1761:
1758:
1746:
1742:
1736:
1732:
1727:
1723:
1718:
1714:
1711:
1705:
1700:
1696:
1653:
1652:Other diagrams
1650:
1622:
1621:
1618:
1611:
1609:
1606:
1599:
1597:
1594:
1587:
1585:
1582:
1575:
1571:
1568:
1567:
1566:
1560:
1553:
1551:
1488:
1481:
1479:
1476:
1465:
1458:
1456:
1453:
1446:
1444:
1441:
1434:
1432:
1429:
1422:
1420:
1413:
1406:
1385:
1384:
1377:
1347:
1307:
1277:
1250:
1247:
1246:
1245:
1242:
1235:
1233:
1230:
1223:
1217:
1216:
1205:
1202:
1198:
1195:
1192:
1189:
1186:
1176:
1165:
1162:
1158:
1155:
1152:
1149:
1146:
1136:
1125:
1122:
1118:
1115:
1111:
1108:
1105:
1102:
1099:
1073:dairy products
1034:
1033:
1021:
1018:
1015:
1009:
1001:
997:
983:
976:
974:
962:
959:
956:
950:
944:
941:
936:
932:
910:
903:
901:
889:
883:
877:
864:
857:
855:
843:
840:
837:
821:
814:
812:
800:
797:
794:
778:
771:
768:
767:
766:
758:
755:
697:Symbolic Logic
648:Leonhard Euler
644:Euler diagrams
590:
587:
541:
538:
519:Euler diagrams
450:
447:
443:Symbolic Logic
433:Leonhard Euler
376:
375:
373:
372:
365:
358:
350:
347:
346:
345:
344:
339:
331:
330:
329:
328:
323:
321:Bayes' theorem
318:
313:
308:
303:
295:
294:
293:
292:
287:
282:
277:
269:
268:
267:
266:
265:
264:
259:
254:
252:Observed value
249:
244:
239:
237:Expected value
234:
229:
219:
214:
213:
212:
207:
202:
197:
192:
187:
177:
176:
175:
165:
164:
163:
158:
153:
148:
143:
133:
128:
120:
119:
118:
117:
112:
107:
106:
105:
95:
94:
93:
80:
79:
71:
70:
64:
63:
44:(upper left),
40:shared by the
26:
9:
6:
4:
3:
2:
5582:
5571:
5568:
5566:
5563:
5561:
5558:
5556:
5553:
5552:
5550:
5536:
5526:
5523:
5521:
5518:
5516:
5513:
5511:
5508:
5506:
5503:
5501:
5498:
5496:
5493:
5491:
5488:
5486:
5483:
5481:
5478:
5477:
5474:
5465:
5460:
5458:
5453:
5451:
5446:
5445:
5442:
5430:
5429:Ernst Zermelo
5427:
5425:
5422:
5420:
5417:
5415:
5414:Willard Quine
5412:
5410:
5407:
5405:
5402:
5400:
5397:
5395:
5392:
5390:
5387:
5385:
5382:
5380:
5377:
5375:
5372:
5371:
5369:
5367:
5366:Set theorists
5363:
5357:
5354:
5352:
5349:
5347:
5344:
5343:
5341:
5335:
5333:
5330:
5329:
5326:
5318:
5315:
5313:
5312:Kripke–Platek
5310:
5306:
5303:
5302:
5301:
5298:
5297:
5296:
5293:
5289:
5286:
5285:
5284:
5283:
5279:
5275:
5272:
5271:
5270:
5267:
5266:
5263:
5260:
5258:
5255:
5253:
5250:
5248:
5245:
5244:
5242:
5238:
5232:
5229:
5227:
5224:
5222:
5219:
5217:
5215:
5210:
5208:
5205:
5203:
5200:
5197:
5193:
5190:
5188:
5185:
5181:
5178:
5176:
5173:
5171:
5168:
5167:
5166:
5163:
5160:
5156:
5153:
5151:
5148:
5146:
5143:
5141:
5138:
5137:
5135:
5132:
5128:
5122:
5119:
5117:
5114:
5112:
5109:
5107:
5104:
5102:
5099:
5097:
5094:
5092:
5089:
5085:
5082:
5080:
5077:
5076:
5075:
5072:
5070:
5067:
5065:
5062:
5060:
5057:
5055:
5052:
5049:
5045:
5042:
5040:
5037:
5035:
5032:
5031:
5029:
5023:
5020:
5019:
5016:
5010:
5007:
5005:
5002:
5000:
4997:
4995:
4992:
4990:
4987:
4985:
4982:
4980:
4977:
4974:
4971:
4969:
4966:
4965:
4963:
4961:
4957:
4949:
4948:specification
4946:
4944:
4941:
4940:
4939:
4936:
4935:
4932:
4929:
4927:
4924:
4922:
4919:
4917:
4914:
4912:
4909:
4907:
4904:
4902:
4899:
4897:
4894:
4890:
4887:
4886:
4885:
4882:
4880:
4877:
4873:
4870:
4868:
4865:
4863:
4860:
4859:
4858:
4855:
4853:
4850:
4849:
4847:
4845:
4841:
4836:
4826:
4823:
4822:
4820:
4816:
4812:
4805:
4800:
4798:
4793:
4791:
4786:
4785:
4782:
4772:
4771:
4766:
4758:
4752:
4749:
4747:
4744:
4742:
4739:
4737:
4734:
4730:
4727:
4726:
4725:
4722:
4720:
4717:
4715:
4712:
4710:
4706:
4703:
4701:
4698:
4696:
4693:
4691:
4688:
4686:
4683:
4682:
4680:
4676:
4670:
4667:
4665:
4662:
4660:
4659:Recursive set
4657:
4655:
4652:
4650:
4647:
4645:
4642:
4640:
4637:
4633:
4630:
4628:
4625:
4623:
4620:
4618:
4615:
4613:
4610:
4609:
4608:
4605:
4603:
4600:
4598:
4595:
4593:
4590:
4588:
4585:
4583:
4580:
4579:
4577:
4575:
4571:
4565:
4562:
4560:
4557:
4555:
4552:
4550:
4547:
4545:
4542:
4540:
4537:
4535:
4532:
4528:
4525:
4523:
4520:
4518:
4515:
4514:
4513:
4510:
4508:
4505:
4503:
4500:
4498:
4495:
4493:
4490:
4488:
4485:
4481:
4478:
4477:
4476:
4473:
4469:
4468:of arithmetic
4466:
4465:
4464:
4461:
4457:
4454:
4452:
4449:
4447:
4444:
4442:
4439:
4437:
4434:
4433:
4432:
4429:
4425:
4422:
4420:
4417:
4416:
4415:
4412:
4411:
4409:
4407:
4403:
4397:
4394:
4392:
4389:
4387:
4384:
4382:
4379:
4376:
4375:from ZFC
4372:
4369:
4367:
4364:
4358:
4355:
4354:
4353:
4350:
4348:
4345:
4343:
4340:
4339:
4338:
4335:
4333:
4330:
4328:
4325:
4323:
4320:
4318:
4315:
4313:
4310:
4308:
4305:
4304:
4302:
4300:
4296:
4286:
4285:
4281:
4280:
4275:
4274:non-Euclidean
4272:
4268:
4265:
4263:
4260:
4258:
4257:
4253:
4252:
4250:
4247:
4246:
4244:
4240:
4236:
4233:
4231:
4228:
4227:
4226:
4222:
4218:
4215:
4214:
4213:
4209:
4205:
4202:
4200:
4197:
4195:
4192:
4190:
4187:
4185:
4182:
4180:
4177:
4176:
4174:
4170:
4169:
4167:
4162:
4156:
4151:Example
4148:
4140:
4135:
4134:
4133:
4130:
4128:
4125:
4121:
4118:
4116:
4113:
4111:
4108:
4106:
4103:
4102:
4101:
4098:
4096:
4093:
4091:
4088:
4086:
4083:
4079:
4076:
4074:
4071:
4070:
4069:
4066:
4062:
4059:
4057:
4054:
4052:
4049:
4047:
4044:
4043:
4042:
4039:
4037:
4034:
4030:
4027:
4025:
4022:
4020:
4017:
4016:
4015:
4012:
4008:
4005:
4003:
4000:
3998:
3995:
3993:
3990:
3988:
3985:
3983:
3980:
3979:
3978:
3975:
3973:
3970:
3968:
3965:
3963:
3960:
3956:
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3937:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3914:
3911:
3909:
3908:by definition
3906:
3905:
3904:
3901:
3897:
3894:
3893:
3892:
3889:
3887:
3884:
3882:
3879:
3877:
3874:
3872:
3869:
3868:
3865:
3862:
3860:
3856:
3851:
3845:
3841:
3831:
3828:
3826:
3823:
3821:
3818:
3816:
3813:
3811:
3808:
3806:
3803:
3801:
3798:
3796:
3795:Kripke–Platek
3793:
3791:
3788:
3784:
3781:
3779:
3776:
3775:
3774:
3771:
3770:
3768:
3764:
3756:
3753:
3752:
3751:
3748:
3746:
3743:
3739:
3736:
3735:
3734:
3731:
3729:
3726:
3724:
3721:
3719:
3716:
3714:
3711:
3708:
3704:
3700:
3697:
3693:
3690:
3688:
3685:
3683:
3680:
3679:
3678:
3674:
3671:
3670:
3668:
3666:
3662:
3658:
3650:
3647:
3645:
3642:
3640:
3639:constructible
3637:
3636:
3635:
3632:
3630:
3627:
3625:
3622:
3620:
3617:
3615:
3612:
3610:
3607:
3605:
3602:
3600:
3597:
3595:
3592:
3590:
3587:
3585:
3582:
3580:
3577:
3575:
3572:
3571:
3569:
3567:
3562:
3554:
3551:
3549:
3546:
3544:
3541:
3539:
3536:
3534:
3531:
3529:
3526:
3525:
3523:
3519:
3516:
3514:
3511:
3510:
3509:
3506:
3504:
3501:
3499:
3496:
3494:
3491:
3489:
3485:
3481:
3479:
3476:
3472:
3469:
3468:
3467:
3464:
3463:
3460:
3457:
3455:
3451:
3441:
3438:
3436:
3433:
3431:
3428:
3426:
3423:
3421:
3418:
3416:
3413:
3409:
3406:
3405:
3404:
3401:
3397:
3392:
3391:
3390:
3387:
3386:
3384:
3382:
3378:
3370:
3367:
3365:
3362:
3360:
3357:
3356:
3355:
3352:
3350:
3347:
3345:
3342:
3340:
3337:
3335:
3332:
3330:
3327:
3325:
3322:
3321:
3319:
3317:
3316:Propositional
3313:
3307:
3304:
3302:
3299:
3297:
3294:
3292:
3289:
3287:
3284:
3282:
3279:
3275:
3272:
3271:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3244:Logical truth
3242:
3240:
3237:
3236:
3234:
3232:
3228:
3225:
3223:
3219:
3213:
3210:
3208:
3205:
3203:
3200:
3198:
3195:
3193:
3190:
3188:
3184:
3180:
3176:
3174:
3171:
3169:
3166:
3164:
3160:
3157:
3156:
3154:
3152:
3146:
3141:
3135:
3132:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3073:
3070:
3069:
3068:
3065:
3064:
3062:
3058:
3054:
3047:
3042:
3040:
3035:
3033:
3028:
3027:
3024:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2998:
2995:
2993:
2989:
2986:
2982:
2978:
2977:
2972:
2968:
2967:
2949:
2945:
2941:
2936:
2931:
2927:
2923:
2922:Ruskey, Frank
2918:
2914:
2908:
2904:
2900:
2896:
2892:
2888:
2882:
2878:
2877:W. H. Freeman
2874:
2870:
2866:
2862:
2858:
2853:
2847:
2843:
2839:
2834:
2830:
2826:
2825:
2824:New Scientist
2820:
2816:
2806:on 2017-05-01
2802:
2798:
2791:
2787:
2783:
2782:
2768:
2762:
2758:
2754:
2750:
2749:
2744:
2737:
2729:
2723:
2719:
2715:
2711:
2705:
2690:
2686:
2682:
2678:
2674:
2673:
2668:
2661:
2652:
2646:
2642:
2638:
2637:
2632:
2626:
2624:
2622:
2606:
2600:
2586:
2582:
2575:
2561:on 2009-04-29
2560:
2556:
2550:
2542:
2538:
2537:
2529:
2525:
2521:
2517:
2516:Ruskey, Frank
2511:
2503:
2499:
2495:
2491:
2487:
2483:
2482:
2477:
2471:
2463:
2459:
2458:
2453:
2447:
2445:
2443:
2434:
2430:
2423:
2421:
2405:on 2017-04-14
2401:
2397:
2390:
2389:
2381:
2367:
2363:
2359:
2358:
2353:
2347:
2345:
2336:
2332:
2328:
2322:
2314:
2310:
2306:
2302:
2298:
2294:
2290:
2286:
2285:
2280:
2274:
2272:
2263:
2262:
2257:
2253:
2252:Ruskey, Frank
2247:
2245:
2229:
2225:
2218:
2211:
2209:
2200:
2196:
2195:
2190:
2186:
2180:
2178:
2171:
2169:
2162:
2158:
2154:
2150:
2146:
2145:
2137:
2134:(July 1880).
2133:
2127:
2125:
2110:
2109:
2104:
2098:
2090:
2083:
2076:
2062:
2058:
2052:
2050:
2035:on 2020-08-04
2034:
2030:
2026:
2020:
2016:
2002:
1998:
1994:
1993:pages 95-126.
1990:
1984:
1980:
1970:
1967:
1965:
1964:Vesica piscis
1962:
1960:
1957:
1955:
1952:
1950:
1947:
1944:
1941:
1938:
1934:
1930:
1927:
1925:
1922:
1920:
1917:
1914:
1910:
1907:
1906:
1900:
1898:
1882:
1879:
1876:
1856:
1853:
1850:
1842:
1833:
1824:
1822:
1818:
1814:
1810:
1806:
1793:
1785:
1782:
1774:
1771:
1768:
1765:
1762:
1759:
1756:
1744:
1740:
1734:
1730:
1725:
1721:
1716:
1712:
1709:
1703:
1698:
1694:
1685:
1681:
1677:
1673:
1671:
1667:
1663:
1659:
1649:
1647:
1646:stained-glass
1643:
1639:
1635:
1631:
1626:
1615:
1610:
1603:
1598:
1591:
1586:
1579:
1574:
1573:
1564:
1557:
1552:
1547:
1543:
1539:
1535:
1531:
1526:
1521:
1517:
1513:
1509:
1505:
1500:
1496:
1492:
1485:
1480:
1474:
1472:
1471:Euler diagram
1468:
1462:
1457:
1450:
1445:
1438:
1433:
1426:
1421:
1417:
1410:
1405:
1404:
1403:
1401:
1397:
1393:
1382:
1378:
1376:
1374:
1369:
1364:
1359:
1352:
1348:
1346:
1344:
1339:
1334:
1329:
1324:
1319:
1312:
1308:
1306:
1304:
1299:
1294:
1289:
1282:
1278:
1275:
1271:
1270:
1267:
1265:
1261:
1257:
1239:
1234:
1231:Euler diagram
1227:
1222:
1221:
1220:
1200:
1196:
1193:
1187:
1184:
1177:
1160:
1156:
1153:
1147:
1144:
1137:
1120:
1116:
1113:
1109:
1106:
1100:
1097:
1090:
1089:
1088:
1085:
1082:
1078:
1074:
1069:
1064:
1062:
1058:
1054:
1050:
1046:
1041:
1019:
1013:
1007:
999:
995:
986:
980:
975:
960:
954:
948:
942:
939:
934:
930:
921:
917:
913:
907:
902:
887:
875:
867:
861:
856:
841:
838:
835:
824:
818:
813:
798:
795:
792:
781:
775:
770:
769:
764:
754:
752:
747:
745:
741:
737:
733:
729:
726:implied that
725:
721:
717:
713:
708:
706:
702:
698:
694:
690:
688:
684:
680:
676:
672:
668:
664:
659:
657:
656:Boolean logic
651:
649:
645:
641:
637:
633:
628:
626:
622:
618:
614:
610:
603:
599:
598:Stained-glass
595:
586:
580:
579:
571:, denoted by
570:
569:
563:
559:
556:
546:
537:
535:
531:
527:
522:
520:
515:
513:
509:
505:
501:
497:
494: ∩
493:
489:
485:
481:
477:
473:
468:
464:
460:
459:logic diagram
456:
446:
444:
440:
439:
434:
430:
426:
421:
419:
415:
411:
407:
403:
399:
395:
391:
387:
383:
371:
366:
364:
359:
357:
352:
351:
349:
348:
343:
340:
338:
335:
334:
333:
332:
327:
324:
322:
319:
317:
314:
312:
309:
307:
304:
302:
299:
298:
297:
296:
291:
288:
286:
283:
281:
278:
276:
273:
272:
271:
270:
263:
260:
258:
255:
253:
250:
248:
245:
243:
240:
238:
235:
233:
230:
228:
225:
224:
223:
220:
218:
215:
211:
208:
206:
203:
201:
198:
196:
193:
191:
188:
186:
183:
182:
181:
178:
174:
171:
170:
169:
166:
162:
159:
157:
154:
152:
149:
147:
144:
142:
139:
138:
137:
134:
132:
129:
127:
124:
123:
122:
121:
116:
113:
111:
110:Indeterminism
108:
104:
101:
100:
99:
96:
92:
89:
88:
87:
84:
83:
82:
81:
77:
73:
72:
69:
66:
65:
62:
58:
57:
51:
47:
43:
39:
34:
30:
19:
18:Venn diagrams
5495:Karnaugh map
5480:Venn diagram
5479:
5379:Georg Cantor
5374:Paul Bernays
5305:Morse–Kelley
5280:
5213:
5212:Subset
5159:hereditarily
5121:Venn diagram
5120:
5079:ordered pair
4994:Intersection
4938:Axiom schema
4761:
4559:Ultraproduct
4406:Model theory
4371:Independence
4307:Formal proof
4299:Proof theory
4282:
4255:
4212:real numbers
4184:second-order
4095:Substitution
3972:Metalanguage
3913:conservative
3886:Axiom schema
3830:Constructive
3800:Morse–Kelley
3766:Set theories
3745:Aleph number
3738:inaccessible
3644:Grothendieck
3528:intersection
3415:Higher-order
3403:Second-order
3349:Truth tables
3306:Venn diagram
3305:
3089:Formal proof
2992:Cut-the-knot
2974:
2952:. Retrieved
2903:A. K. Peters
2898:
2868:
2861:Stewart, Ian
2837:
2828:
2822:
2808:. Retrieved
2801:the original
2796:
2747:
2736:
2713:
2704:
2693:. Retrieved
2676:
2670:
2660:
2635:
2609:. Retrieved
2599:
2588:. Retrieved
2584:
2574:
2563:. Retrieved
2559:the original
2549:
2540:
2534:
2510:
2485:
2479:
2470:
2460:. Berkeley:
2456:
2428:
2407:. Retrieved
2400:the original
2387:
2380:
2369:. Retrieved
2356:
2334:
2321:
2288:
2282:
2259:
2232:. Retrieved
2223:
2198:
2192:
2151:(59): 1–18.
2148:
2142:
2112:. Retrieved
2106:
2097:
2088:
2080:Venn, John.
2075:
2064:. Retrieved
2060:
2037:. Retrieved
2033:the original
2028:
2019:
2000:
1988:
1983:
1937:Karnaugh map
1933:Veitch chart
1841:truth tables
1838:
1807:
1679:
1674:
1655:
1641:
1637:
1633:
1629:
1623:
1545:
1541:
1537:
1533:
1529:
1524:
1519:
1515:
1511:
1507:
1503:
1498:
1467:Non-example:
1466:
1399:
1391:
1388:
1355:
1315:
1285:
1252:
1243:Venn diagram
1218:
1086:
1080:
1076:
1075:and another
1072:
1067:
1065:
1053:intersection
1052:
1042:
1038:
919:
915:
868:of two sets
825:of two sets
782:of two sets
780:Intersection
748:
743:
739:
735:
732:prime number
727:
719:
715:
709:
704:
696:
691:
686:
682:
681:. Hence, no
678:
674:
670:
666:
660:
652:
629:
625:Frank Ruskey
621:formal logic
617:propositions
612:
606:
578:intersection
576:
566:
564:
560:
554:
551:
534:Venn diagram
533:
529:
525:
523:
516:
511:
507:
503:
499:
495:
491:
487:
483:
479:
475:
471:
462:
458:
454:
452:
442:
436:
428:
422:
382:Venn diagram
381:
379:
342:Tree diagram
337:Venn diagram
336:
301:Independence
247:Markov chain
131:Sample space
29:
5515:Truth table
5404:Thomas Jech
5247:Alternative
5226:Uncountable
5180:Ultrafilter
5039:Cardinality
4943:replacement
4884:Determinacy
4669:Type theory
4617:undecidable
4549:Truth value
4436:equivalence
4115:non-logical
3728:Enumeration
3718:Isomorphism
3665:cardinality
3649:Von Neumann
3614:Ultrafilter
3579:Uncountable
3513:equivalence
3430:Quantifiers
3420:Fixed-point
3389:First-order
3269:Consistency
3254:Proposition
3231:Traditional
3202:Lindström's
3192:Compactness
3134:Type theory
3079:Cardinality
2842:Focal Press
2524:Wagon, Stan
1987:In Euler's
1057:cardinality
987:of A in U
632:Ramon Llull
455:set diagram
414:linguistics
402:probability
257:Random walk
98:Determinism
86:Probability
5549:Categories
5399:Kurt Gödel
5384:Paul Cohen
5221:Transitive
4989:Identities
4973:Complement
4960:Operations
4921:Regularity
4889:projective
4852:Adjunction
4811:Set theory
4480:elementary
4173:arithmetic
4041:Quantifier
4019:functional
3891:Expression
3609:Transitive
3553:identities
3538:complement
3471:hereditary
3454:Set theory
2954:2017-05-01
2810:2017-05-01
2755:. p.
2743:"3.3 Laws"
2716:. Boston:
2695:2020-05-12
2611:2008-08-13
2590:2020-09-05
2565:2009-06-20
2409:2017-04-14
2394:(Thesis).
2371:2013-04-09
2364:. p.
2352:Venn, John
2234:2009-10-26
2224:MAA Online
2185:Venn, John
2132:Venn, John
2114:2021-08-06
2066:2020-09-05
2039:2020-09-05
2011:References
1969:UpSet plot
1897:R-diagrams
1670:hypercubes
1583:Three sets
918:(left) in
761:See also:
490:, denoted
410:statistics
398:set theory
168:Experiment
115:Randomness
61:statistics
5332:Paradoxes
5252:Axiomatic
5231:Universal
5207:Singleton
5202:Recursive
5145:Countable
5140:Amorphous
4999:Power set
4916:Power set
4867:dependent
4862:countable
4751:Supertask
4654:Recursion
4612:decidable
4446:saturated
4424:of models
4347:deductive
4342:axiomatic
4262:Hilbert's
4249:Euclidean
4230:canonical
4153:axiomatic
4085:Signature
4014:Predicate
3903:Extension
3825:Ackermann
3750:Operation
3629:Universal
3619:Recursive
3594:Singleton
3589:Inhabited
3574:Countable
3564:Types of
3548:power set
3518:partition
3435:Predicate
3381:Predicate
3296:Syllogism
3286:Soundness
3259:Inference
3249:Tautology
3151:paradoxes
2981:EMS Press
2935:1207.6452
2362:Macmillan
2313:125364002
1959:Triquetra
1880:∈
1854:∈
1786:∈
1772:−
1766:≤
1760:≤
1713:
1607:Five sets
1595:Four sets
1416:Gray code
1260:tesseract
1061:schematic
1017:∖
958:∖
940:∩
882:△
839:∪
796:∩
663:syllogism
609:John Venn
427:in 1712 (
394:John Venn
161:Singleton
5560:Diagrams
5336:Problems
5240:Theories
5216:Superset
5192:Infinite
5021:Concepts
4901:Infinity
4818:Overview
4736:Logicism
4729:timeline
4705:Concrete
4564:Validity
4534:T-schema
4527:Kripke's
4522:Tarski's
4517:semantic
4507:Strength
4456:submodel
4451:spectrum
4419:function
4267:Tarski's
4256:Elements
4243:geometry
4199:Robinson
4120:variable
4105:function
4078:spectrum
4068:Sentence
4024:variable
3967:Language
3920:Relation
3881:Automata
3871:Alphabet
3855:language
3709:-jection
3687:codomain
3673:Function
3634:Universe
3604:Infinite
3508:Relation
3291:Validity
3281:Argument
3179:theorem,
2948:Archived
2712:(2004).
2689:Archived
2633:(2004).
2454:(1918).
2354:(1881).
2201:: 47–59.
2187:(1880).
2161:Archived
2003:(1712)).
1903:See also
1666:polygons
1642:cogwheel
1619:Six sets
1527:denotes
1523:, while
1501:denotes
1396:ellipses
922:(right)
757:Overview
751:new math
669:is some
467:elements
461:, shows
242:Variance
5274:General
5269:Zermelo
5175:subbase
5157: (
5096:Forcing
5074:Element
5046: (
5024:Methods
4911:Pairing
4678:Related
4475:Diagram
4373: (
4352:Hilbert
4337:Systems
4332:Theorem
4210:of the
4155:systems
3935:Formula
3930:Grammar
3846: (
3790:General
3503:Forcing
3488:Element
3408:Monadic
3183:paradox
3124:Theorem
3060:General
2983:, 2001
2940:Bibcode
2502:2311865
2333:(ed.).
2305:3614533
1392:elegant
1264:16-cell
1256:simplex
1077:cheeses
1045:circles
685:is any
677:is any
665:: 'All
589:History
540:Example
449:Details
386:diagram
156:Outcome
5165:Filter
5155:Finite
5091:Family
5034:Almost
4872:global
4857:Choice
4844:Axioms
4441:finite
4204:Skolem
4157:
4132:Theory
4100:Symbol
4090:String
4073:atomic
3950:ground
3945:closed
3940:atomic
3896:ground
3859:syntax
3755:binary
3682:domain
3599:Finite
3364:finite
3222:Logics
3181:
3129:Theory
2909:
2883:
2848:
2763:
2724:
2647:
2500:
2311:
2303:
1081:cheese
1049:wooden
1011:
1005:
952:
946:
885:
879:
833:
790:
730:was a
722:-fold
530:scaled
431:) and
103:System
91:Axioms
38:glyphs
5257:Naive
5187:Fuzzy
5150:Empty
5133:types
5084:tuple
5054:Class
5048:large
5009:Union
4926:Union
4431:Model
4179:Peano
4036:Proof
3876:Arity
3805:Naive
3692:image
3624:Fuzzy
3584:Empty
3533:union
3478:Class
3119:Model
3109:Lemma
3067:Axiom
2930:arXiv
2804:(PDF)
2793:(PDF)
2531:(PDF)
2498:JSTOR
2403:(PDF)
2392:(PDF)
2309:S2CID
2301:JSTOR
2230:(MAA)
2220:(PDF)
2164:(PDF)
2147:. 5.
2139:(PDF)
2085:(PDF)
1975:Notes
1469:This
823:Union
673:. No
583:A ∩ B
573:A ∪ B
568:union
406:logic
136:Event
46:Latin
42:Greek
5170:base
4554:Type
4357:list
4161:list
4138:list
4127:Term
4061:rank
3955:open
3849:list
3661:Maps
3566:sets
3425:Free
3395:list
3145:list
3072:list
2907:ISBN
2881:ISBN
2846:ISBN
2761:ISBN
2722:ISBN
2645:ISBN
1935:and
1911:(by
1684:sine
528:(or
510:and
502:and
486:and
416:and
390:sets
5131:Set
4241:of
4223:of
4171:of
3703:Sur
3677:Map
3484:Ur-
3466:Set
2990:at
2829:121
2681:doi
2490:doi
2366:108
2293:doi
2153:doi
1710:sin
1525:BCE
1475:not
1473:is
1400:any
914:of
689:.'
555:and
463:all
457:or
5551::
4627:NP
4251::
4245::
4175::
3852:),
3707:Bi
3699:In
2979:,
2973:,
2946:.
2938:.
2867:.
2827:.
2795:.
2759:.
2757:62
2745:.
2687:.
2677:40
2675:.
2669:.
2620:^
2583:.
2541:53
2539:.
2533:.
2522:;
2518:;
2496:.
2486:70
2484:.
2441:^
2419:^
2360:.
2343:^
2307:.
2299:.
2289:53
2287:.
2270:^
2258:.
2243:^
2226:.
2222:.
2207:^
2197:.
2191:.
2176:^
2159:.
2149:10
2141:.
2123:^
2105:.
2087:.
2059:.
2048:^
2027:.
1899:.
1869:,
1672:.
1544:∩
1540:∩
1536:∩
1532:∩
1518:∩
1514:∩
1510:∩
1506:∩
707:.
585:.
536:.
532:)
514:.
412:,
408:,
404:,
380:A
5463:e
5456:t
5449:v
5214:·
5198:)
5194:(
5161:)
5050:)
4803:e
4796:t
4789:v
4707:/
4622:P
4377:)
4163:)
4159:(
4056:∀
4051:!
4046:∃
4007:=
4002:↔
3997:→
3992:∧
3987:∨
3982:¬
3705:/
3701:/
3675:/
3486:)
3482:(
3369:∞
3359:3
3147:)
3045:e
3038:t
3031:v
2957:.
2942::
2932::
2915:.
2889:.
2875:(
2854:.
2813:.
2769:.
2730:.
2698:.
2683::
2655:.
2653:.
2614:.
2593:.
2568:.
2504:.
2492::
2464:.
2412:.
2374:.
2315:.
2295::
2264:.
2237:.
2199:4
2155::
2117:.
2091:.
2069:.
2042:.
1939:)
1915:)
1883:B
1877:x
1857:A
1851:x
1794:.
1790:N
1783:i
1775:1
1769:n
1763:i
1757:0
1745:i
1741:2
1735:)
1731:x
1726:i
1722:2
1717:(
1704:=
1699:i
1695:y
1680:n
1638:z
1634:y
1630:x
1628:(
1549:.
1546:E
1542:D
1538:C
1534:B
1530:A
1520:E
1516:D
1512:C
1508:B
1504:A
1499:A
1204:}
1201:7
1197:,
1194:4
1191:{
1188:=
1185:C
1164:}
1161:6
1157:,
1154:1
1151:{
1148:=
1145:B
1124:}
1121:5
1117:,
1114:2
1110:,
1107:1
1104:{
1101:=
1098:A
1068:n
1020:A
1014:U
1008:=
1000:c
996:A
961:A
955:B
949:=
943:B
935:c
931:A
920:B
916:A
888:B
876:A
842:B
836:A
799:B
793:A
744:n
740:n
736:n
728:n
720:n
716:n
687:C
683:A
679:C
675:B
671:B
667:A
512:T
508:S
504:T
500:S
496:T
492:S
488:T
484:S
480:S
476:S
472:S
435:(
369:e
362:t
355:v
20:)
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