Given the following Venn diagram, find n[ (AUB) nC)]. 21 23 23 6 10 13 с 14 6 B U

Algebra and Trigonometry (6th Edition)
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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### Problem Statement

Given the following Venn diagram, find \( n[(A \cup B)^c \cap C] \).

### Venn Diagram Explanation

The Venn diagram consists of three overlapping circles labeled A, B, and C, all within a universal set U. The diagram includes various regions, each representing the intersection or difference of sets:

- **Region in Circle A only:** 23
- **Region in Circle B only:** 6
- **Region in Circle C only:** 13
- **Intersection of A and B (excluding C):** 6
- **Intersection of A and C (excluding B):** 23
- **Intersection of B and C (excluding A):** 14
- **Intersection of A, B, and C:** 10
- **Outside all circles (only in U):** 21

### Question Options

- \( \circ \) 13
- \( \circ \) 51
- \( \circ \) 46
- \( \circ \) 49
- \( \circ \) 43
- \( \circ \) None of the above.
Transcribed Image Text:### Problem Statement Given the following Venn diagram, find \( n[(A \cup B)^c \cap C] \). ### Venn Diagram Explanation The Venn diagram consists of three overlapping circles labeled A, B, and C, all within a universal set U. The diagram includes various regions, each representing the intersection or difference of sets: - **Region in Circle A only:** 23 - **Region in Circle B only:** 6 - **Region in Circle C only:** 13 - **Intersection of A and B (excluding C):** 6 - **Intersection of A and C (excluding B):** 23 - **Intersection of B and C (excluding A):** 14 - **Intersection of A, B, and C:** 10 - **Outside all circles (only in U):** 21 ### Question Options - \( \circ \) 13 - \( \circ \) 51 - \( \circ \) 46 - \( \circ \) 49 - \( \circ \) 43 - \( \circ \) None of the above.
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