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Thought for the day: To get the full meaning of some prompts, you need to take your time and pay attention to the details.
Concepts: Venn diagrams; sets and subsets; counting combinations; powers of 2 (possibly symmetry)
Examples of noticing and wondering
I notice four main rectangles: red, blue, yellow, and grey.
I notice that the diagram has symmetry.
I notice that this is a Venn diagram made of rectangles rather than circles.
I notice that each region contains a unique combination of colors.
I notice that there are sixteen regions (including the outside part that has no colors).
I wonder if the Venn diagram is complete (contains every possible combination of the four colors).
I wonder if there are other ways to create a complete 4-set Venn diagram.
I wonder if I could make a 4-set Venn Diagram using only circles.
I wonder how many regions a 5-set Venn diagram would need to have.
I wonder if it is possible to make a 5-set Venn diagram.
Notes
Many people are familiar with two- and three-set Venn diagrams. Four-set diagrams may be less familiar, and it is surprisingly hard to create one that includes all possible combinations. Try making one using circles! Most people discover that at least two of the combinations are left out.
This prompt offers a great chance for students to study combinations. The number of regions in a complete Venn diagram follows an interesting pattern. Can you find it and discover what causes it?
Number of Sets Number of Regions
1 2
2 4
3 8
4 16
There are many other interesting things you might wonder! The following list just scratches the surface.
I wonder what is the best way to keep track of the regions so that I don't miss any.
I wonder if a 5-set Venn diagram can have symmetry.
I wonder if it is possible to make all n-set Venn diagrams (where n can be any counting number).