SOLUTION: 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

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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(52855)   (Show Source): You can put this solution on YOUR website!
.
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)
--------------------------------------------- 

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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