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Set Theory

Set Theory​

Two sets:

n(A union B) = n(A) + n(B) - n(A intersection B)

Three sets:

n(A union B union C)
= n(A) + n(B) + n(C)
- n(A intersection B) - n(B intersection C) - n(C intersection A)
+ n(A intersection B intersection C)

Only regions:

Only A = A - AB only - AC only - ABC
Exactly two = AB only + BC only + CA only
At least two = exactly two + all three
At least one = union
None = total - union

Fast Venn method:

  1. Fill the center first.
  2. Fill exactly-two regions by subtracting center from pairwise intersections.
  3. Fill only-one regions.
  4. Use total to get none.