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Venn Diagram for Three Sets and Set Operations

Venn Diagram for Three Sets and Set Operations
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2012-08-18 16:45
CirclePolygonProbability & StatisticsGeometric Construction
In collections Class-10
This GeoGebra example demonstrates a three-set Venn diagram, visually illustrating the relationships among three overlapping sets and their elementary set-theoretic operations. Core concepts include union, intersection, complement, disjoint regions, and set inclusion from elementary set theory. The construction uses GeoGebra commands such as Polygon, Element, IntersectRegion, and Union, together with circle objects C1–C4, point and region objects A1–A4, B1–B4, and set variables set1, set2, set3 to build and highlight the distinct regions of the diagram. It is suitable for high school mathematics, discrete mathematics, and introductory logic courses, serving as an interactive visualization tool for set operations and region analysis.

GeoGebra Commands & Parameters

  1. Polygon(C3, C2, 4) → C, a_2, b_2, c_2, d_2, C1, C4
  2. Polygon(B2, B1, 4) → B, a_1, b_1, c_1, d_1, B4, B3
  3. Polygon(A4, A3, 4) → A, a, b, c, d, A2, A1
  4. Polygon(P, Q, 4) → E, p, q, m, n, R, S
  5. Element(setNames, set1) → text1
  6. Element(setNames, set2) → text2
  7. Element(setNames, set3) → text3
  8. IntersectRegion(Element[sets, set3], Element[sets, set4]) → interSet, l1, r, s, t, D, F, G, T
  9. Element(setNames, set4) → text4
  10. Union(interSet, Element[sets, set1]) → combo1, u, v, w, e, U, V, W, Z
  11. TravelingSalesman(Union[Element[Verts, set3], {Vertex[interSet]}] \ Intersection[Element[Verts, set3], {Vertex[interSet]}]) → Comp34
  12. TravelingSalesman(Union[Element[Verts, set4], {Vertex[interSet]}] \ Intersection[Element[Verts, set4], {Vertex[interSet]}]) → Comp43
  13. Union(Element[sets, set1], Element[sets, set2]) → unionSet, h_1, I, J, K, L, M, N, O, i_2, j_2, f, h, i, j, k, H
  14. IntersectRegion(unionSet, Element[sets, set3]) → combo2, a_3, b_3, c_3, g, A_1, B_1, C_1, D_1