SOLUTION: Let A and B be subsets of a universal set U and suppose n(U) = 200, n(A) = 100, n(B) = 80, and n(A ∩ B) = 40. Compute: n(A ∪ B) n(Ac) n(A ∩ Bc)

Algebra ->  Finite-and-infinite-sets -> SOLUTION: Let A and B be subsets of a universal set U and suppose n(U) = 200, n(A) = 100, n(B) = 80, and n(A ∩ B) = 40. Compute: n(A ∪ B) n(Ac) n(A ∩ Bc)      Log On


   

Question 1201448: Let A and B be subsets of a universal set U and suppose n(U) = 200, n(A) = 100, n(B) = 80, and n(A ∩ B) = 40. Compute:
n(A ∪ B)
n(Ac)
n(A ∩ Bc)
Answer by ikleyn(52879) About Me  (Show Source):
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Let A and B be subsets of a universal set U and suppose n(U) = 200, n(A) = 100, n(B) = 80, and n(A ∩ B) = 40. Compute:
(a) n(A ∪ B)
(b) n(Ac)
(c) n(A ∩ Bc)
~~~~~~~~~~~~~~~~~~~~ 

(a)  n(A U B) = n(A) + n(B) - n(A ∩ B) = 100 + 80 - 40 = 140.


(b)  n(A^c) = n(U) - n(A) = 200 - 100 = 100.


(c)  The set  A ∩ B^c  consists of those elements from A that do not belong to B.

     In other words,  A ∩ Bc = A \ (A ∩ B).


     THEREFORE,  n(A ∩ B^c) = n(A) - n(A ∩ B) = 100 - 40 = 60.

Solved.

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