### Problem Statement:Given the following Venn diagram, find \( n[(B \cap C)^c] \).### Explanation of the Venn Diagram:The diagram consists of three intersecting circles labeled A, B, and C, representing different sets. Each section of the diagram contains numbers representing the number of elements in each specific subset. The universal set U is represented by a rectangle containing all the sets.- **Set A:** - Only A: 23 - A and B but not C: 11 - A and C but not B: 6 - A, B, and C: 14- **Set B:** - Only B: 9 - A and B but not C: 11 - B and C but not A: 15 - A, B, and C: 14- **Set C:** - Only C: 21 - A and C but not B: 6 - B and C but not A: 15 - A, B, and C: 14- **Outside sets A, B, C (In Universal Set U):** 11### Question:Find the number of elements in the complement of the intersection of sets B and C, \( n[(B \cap C)^c] \).### Options:- 15- 81- 25- 29- 85- None of the above.---To solve the problem, determine the elements in \( B \cap C \):- \( B \cap C \) includes the regions: - B and C but not A: 15 - A, B, and C: 14So, \( n(B \cap C) = 15 + 14 = 29 \).Find the complement of \( B \cap C \):- Total in Universal Set U = Sum of all numbers = \( 23 + 11 + 6 + 14 + 9 + 15 + 21 + 11 \)- Calculating \( n(U) \): \( 110 \).- Therefore, \( n[(B \cap C)^c] = n(U) - n(B \cap C) = 110 - 29 = 81 \).Hence, the correct answer is 81.

Answered: Image /qna-images/answer/b166768e-3e9e-4db9-bbaf-6022f09f4d34.jpg

Answered: Given the following Venn diagram, find…

Given the following Venn diagram, find n[ (BNC)c]. 015 11 A 23 6 11 14 21 с 15 9 U

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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