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Venn diagram notation for all other sets except one

I'm trying to find a Venn diagram notation that can illustrate data that is only in a single set.

If I can select data from all the other sets, without knowing how many there are, then I can find the intersection of their complement, to select data only in the targeting set.

My current solution looks like this, but it assumes the existance of sets B and C.

enter image description here

The eventual diagram expecting to look like this:

enter image description here

Solution

  • One way to do it would be by using a system based on regions rather than sets. In your case, it would be the region that belongs to set A but does not belong to any other set. You can find the rationale to do that here. The idea is to express the region as a binary chain where 1 means "belongs to set n" and 0 means "does not belong to set n", where n is determined by the ordering of the sets.

    In your example, you might define A as the last set, and therefore as the last bit. With three sets CBA, your region would be 001. The nice thing about this is that the leading zeroes can be naturally disregarded. Your region would be 1b, not matter how many sets there are (the b is for "binary").

    You might even extend the idea by translating the number to another base. For instance, say that you want to express the region of elements belonging to set B only. With the same ordering as before, it would be 010 or 10b. But you can also express it as a decimal number and say "region 2". This expression would be valid if sets A and B exist, independently of the presence of any other set.