Let A, B, and C be subsets of a universal set U and suppose n(U) = 100, n(A) = 24, n(B) = 26, n(C) = 30, n(A ∩ B) = 8, n(A ∩ C) = 10, n(B ∩ C) = 15, and n(A ∩ B ∩ C) = 4. Compute each of the following. (a)    n[A ∪ (B ∩ C)]   (b)    n((Ac ∩ Bc ∩ Cc)c)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let AB, and C be subsets of a universal set U and suppose n(U) = 100, n(A) = 24, n(B) = 26, n(C) = 30, n(A ∩ B) = 8, n(A ∩ C) = 10, n(B ∩ C) = 15, and n(A ∩ B ∩ C) = 4. Compute each of the following.

(a)    n[A ∪ (B ∩ C)]
 

(b)    n((Ac ∩ Bc ∩ Cc)c
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A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

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