This activity was inspired by this numberphile video by Neil Sloane.
Here are the only distinct three ways you can draw two circles in a Venn diagram.
![](https://lycee.samicharity.co.uk/wp-content/uploads/2024/06/image-4.png)
If we take the universal set to be the positive integers, we can come up with some sets that would fit for A and B for the three examples.
- A = Odd numbers, B = Multiples of 4
- A = Even numbers C= Prime numbers
- A= Even numbers B=Multiples of 4
Note that these choices mean that there is at least one number in each region.
Now for the challenge …
Draw all the different Venn diagrams you can make with three circles, and find rules for them all.
Number of ways can be found here. A picture of them all is here.
Watch the numberphile video to find out how many Jonathan Wild found for 4 and 5 circles. It is a lot more! Nobody knows for 6 …