finite math question!!! please help?
Find a formula for the number of elements in the union of 4 sets that uses:
n(A), n(B), n(C), n(D)
n(A⋂B), n(A⋂C), n(A⋂D), n(B⋂C), n(B⋂D), n(C⋂D)
n(A⋂B⋂C), n(A⋂C⋂D), n(B⋂C⋂D), n(A⋂B⋂D)
- PuzzlingLv 71 month agoFavorite Answer
By the inclusion-exclusion principle:
[n(A) + n(B) + n(C) + n(D)]
- [n(A⋂B) + n(A⋂C) + n(A⋂D) + n(B⋂C) + n(B⋂D) + n(C⋂D)]
+ [n(A⋂B⋂C) + n(A⋂C⋂D) + n(B⋂C⋂D) + n(A⋂B⋂D)]
You include the number of elements in A, B, C and D.
But you then have to exclude all combinations of two sets because those have been *overcounted*.
In doing that, you need to include all combinations of three sets because those have now been *undercounted*.
Finally, exclude the intersection of all 4 sets which again was *overcounted*.Source(s): https://en.wikipedia.org/wiki/Inclusion%E2%80%93ex... https://math.stackexchange.com/questions/688019/wh...