Question 1012991: let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A ∩ B) = 80. Compute:
(a) n(A ∪ B)
(b) n(Ac)
(c) n(A ∩ Bc)
Answer by ikleyn(52847)   (Show Source):
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let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A ∩ B) = 80. Compute:
(a) n(A ∪ B)
(b) n(Ac)
(c) n(A ∩ Bc)
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I will solve n.(a) only.
n(A U B) = n(A) + n(B) - n(A ∩ B) = 200 + 160 - 80 = 280.
Explanation: when we take the sum n(A) + n(B), we count elements in the intersection twice.
Therefore, we distract the number of elements in the intersection to compensate what we counted twice.
See the lesson Counting elements in sub-sets of a given finite set in this site.
Similar solved problems are considered there.
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