Problem

Thinking along the lines of Exercise, what do you expect to be the maximum number of regio...

Thinking along the lines of Exercise, what do you expect to be the maximum number of regions possible for a Venn diagram with four sets? Name them as in Exercise. Which of these regions are missing in the given Venn diagram with four sets?

 

Notice that if a Venn diagram has one set A, then it divides the universal set into two regions, A and A'. If the diagram has two sets A and B, then there will be four regions: AB, AB′, A′ ∩ B, and A′ ∩ B′ What is the maximum number of regions for a three-set Venn diagram? Name the regions in a manner similar to what we have just done to one- and two-set Venn diagrams.

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