SOLUTION: PLEASE HELP im Stuck on this problem. Thank You Let A, B, and C be subsets of a universal set U and suppose n(U) = 150, n(A) = 23, n(B) = 25, n(C) = 29, n(A ∩ B) = 8, n(A

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Question 429443: PLEASE HELP im Stuck on this problem. Thank You
Let A, B, and C be subsets of a universal set U and suppose n(U) = 150, n(A) = 23, n(B) = 25, n(C) = 29, n(A ∩ B) = 8, n(A ∩ C) = 9, n(B ∩ C) = 14, and n(A ∩ B ∩ C) = 5
(a) n[A ∩ (B U C)]
(b) n[A ∩ (B U C)c]
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(a) n(A ∩ (B U C)) = n((A ∩B) U (A ∩C))
= n(A ∩B) + n(A ∩C) - n(A ∩ B ∩ C)
= 8 + 9 - 5 = 12.
(b) B+U+C and %28B+U+C%29%5Ec are disjoint, hence so are A ∩ B+U+C and A ∩ %28B+U+C%29%5Ec.
==> nA = n(A ∩ B+U+C ) + n(A ∩ %28B+U+C%29%5Ec)
==> 23 = 12 + n(A ∩ %28B+U+C%29%5Ec)
==> n(A ∩ %28B+U+C%29%5Ec) = 11.