**Venn Diagram Construction for Sets****Objective:**Construct a Venn diagram illustrating the following sets:- \( U = \{1, 2, 3, 4, 5, 6, 7, 8\} \)- \( Y = \{1, 4, 6\} \)- \( Z = \{2, 4, 5, 8\} \)**Diagram Explanation:**The diagram contains a rectangular box labeled \( U \) which represents the universal set. Within this box:- A red circle labeled \( Y \) represents set \( Y \).- A blue circle labeled \( Z \) represents set \( Z \).**Overlap and Elements:**- **Intersection (shared elements):** The area where the red and blue circles overlap contains the element 4, which is common to both sets \( Y \) and \( Z \).- **Unique to \( Y \):** Elements 1 and 6 are in the red circle outside of the overlap.- **Unique to \( Z \):** Elements 2, 5, and 8 are in the blue circle outside of the overlap. **External Elements:**- Elements 3 and 7 lie outside both circles, representing members of the universal set \( U \) that are not part of sets \( Y \) or \( Z \).This Venn diagram visually demonstrates how the elements are distributed across the different sets and their intersections.

Given U=1 , 2 , 3 , 4 , 4, 5 , 6 , 7 , 8 Y=1, 4 , 6Z=2 , 4 , 5 , 6clearly Y∩Z= 4

Answered: Construct a Venn diagram illustrating…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Construct a Venn diagram illustrating the sets below. U={1, 2, 3, 4, 5, 6, 7, 8} Y={1,4, 6} Z3{2,4,5,8}