Let A, B, and C be sets in a universal set U. We are given n(U) = 66, n(A) = 39, n(B) = 37, n(C) = 33, n(A ∩ B) = 21, n(A ∩ C) = 20, n(B ∩ C) = 21, n(A ∩ B ∩ CC) = 8. Find the following values. (a) n((A ∪ B ∪ C)C) (b) n(AC ∩ BC ∩ C)

Let A, B, and C be sets in a universal set U. We are given n(U) = 66, n(A) = 39, n(B) = 37, n(C) = 33, n(A ∩ B) = 21, n(A ∩ C) = 20, n(B ∩ C) = 21, n(A ∩ B ∩ CC) = 8. Find the following values. (a) n((A ∪ B ∪ C)C) (b) n(AC ∩ BC ∩ C)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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Let A, B, and C be sets in a universal set U. We are given n(U) = 66, n(A) = 39, n(B) = 37, n(C) = 33, n(A ∩ B) = 21, n(A ∩ C) = 20, n(B ∩ C) = 21, n(A ∩ B ∩ C^C) = 8. Find the following values.

(a) n((A ∪ B ∪ C)^C)

(b) n(A^C ∩ B^C ∩ C)

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