Note: The video for this module contains a summary of all the concepts covered in the Set Theory lesson. The video would serve as a good revision. Please watch this video in intervals of a few weeks so that you do not forget the concepts. Below is a cheatsheet that includes all the formulae but not necessarily the concepts covered in the video.
8. Cheatsheet
1) n(A∪B) =n(A)+n(B)−n(A∩B)
2) n(A∪B∪C) =n(A)+n(B)+n(c)−n(A∩B)−n(B∩C)−n(A∩C) + n(A∩B∩C)
3) Where P, Q and R are the number of elements in exactly 1, exactly 2 and all 3 sets respectively,
(a) n(A ∪ B ∪ C) = P + Q + R
(b) n(A) + n(B) + n(C) = P + 2Q + 3R
4) Where P, Q, R and S are the number of elements in exactly 1, exactly 2, exactly 3 and all 4 sets respectively,
(a) n(A ∪ B ∪ C ∪ D) = P + Q + R + S
(b) n(A) + n(B) + n(C) + n(D) =
P + 2Q + 3R + 4S
5) When number of elements in each set (i.e., n(A), n(B), ...) and that of universal set (i.e., n(U)) are given, then
1) Maximum number of elements in all sets = Minimum of (n(A),n(B),...)
2) Minimum number of elements in all sets = U−n(A) + n(B) +...)
(Note: n(A) = 100−n(A), n(B) =100−n(B),...)
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