Question 1121888: Sets X and Y are subsets of universal set U. If n(U)=60, n(X)=25, n(Y)=26, and n(X′∩Y)=15, find the number of elements in the following sets.
What is n(X′∩Y′)?
What is n(X′∪Y′)?
Answer by greenestamps(13200)   (Show Source):
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Given: n(U)=60, n(X)=25, n(Y)=26, and n(X′∩Y)=15
n(Y)=26 and n(X′∩Y)=15 --> n(X∩Y)=11
Then n(X)=25 and n(X∩Y)=11 --> n(X∩Y′)=14
(1) What is n(X′∩Y′)?
This set contains everything that is not in either X, or Y, or both:
n(X′∩Y′) = n(U)-n(X′∩Y)-n(X∩Y)-n(X∩Y′) = 60-15-11-14 = 20
(2) What is n(X′∪Y′)?
This set contains everything that is either not in X or not in Y -- i.e., it contains everything except what is in BOTH X and Y:
n(X′∪Y′) = n(U)-n(X∩Y) = 60-11 = 49
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