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Venn Diagram with Intersection and Union

Venn Diagram with Intersection and Union
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2020-05-24 13:32
Probability & StatisticsGeometric Construction
This example demonstrates the graphical representation of Venn diagrams, including intersections and unions. It involves core mathematical concepts such as set theory operations (intersection, union) and geometric visualization. The construction utilizes GeoGebra commands and objects like PointIn, Max, Min, Polygon, If, along with elements like EorFoutbase, Fbase, Ucorners, etc., to build and compute regions. It is suitable for high school mathematics or discrete mathematics courses teaching set operations and geometric constructions.

GeoGebra Commands & Parameters

  1. PointIn(Polygon[Fbase + Ucorners]) → Fcorner
  2. PointIn(Polygon[{(0, 0), (10 - Fwidth, 0), (10 - Fwidth, 10 - Fheight), (0, 10 - Fheight)}]) → Fareabase
  3. PointIn(Polygon[Ebase + Ucorners]) → Ecorner
  4. PointIn(Polygon[{(0, 0), (10 - Ewidth, 0), (10 - Ewidth, 10 - Eheight), (0, 10 - Eheight)}]) → Eareabase
  5. Max(Eleft, Fleft) → EFleft
  6. Min(Eright, Fright) → EFright
  7. Max(Ebottom, Fbottom) → EFbottom
  8. Min(Etop, Ftop) → EFtop
  9. Polygon(Ucorners) → Uarea
  10. Polygon(Eareabase + Ecorners) → Earea
  11. Polygon((EFleft, EFbottom) + EFcorners) → EFrect
  12. Polygon(Fareabase + Fcorners) → Farea
  13. If(noshowEF, 0, EFrect) → EFarea
  14. Polygon(Ebase + Ecorners) → Erect
  15. Polygon(Fbase + Fcorners) → Frect
  16. Polygon(EandFoutbase + EFcorners) → EandFout
  17. Polygon(EorFoutbase - unioncorner + Eareabase + Ecorners) → Eout
  18. Polygon(EorFoutbase - unioncorner + Fareabase + Fcorners) → Fout

AI Drawing Prompt Reference

Draw a Venn diagram with two overlapping rectangles E and F inside a larger rectangle U. First outline U, then draw the full rectangles for E and F. Highlight the intersection area of E and F with shading or color. Then show the parts of E not in F, the parts of F not in E, and the union of E and F. Clearly distinguish each region and label the intersection and union.
The prompt above was compiled from the original drawing commands and is for reference only.