Question 1012991
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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 &#8745; 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 <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A> in this site.

Similar solved problems are considered there.
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