**Venn Diagram Problem Analysis****Given Problem:**- \( n(A) = 10 \)- \( n(B) = 26 \)- \( n(A \cup B) = 31 \)**Objective:**Use a Venn diagram to find \( n(A \cap B) \).**Explanation:**To solve the problem, we need to find the intersection of sets A and B, \( n(A \cap B) \).**Venn Diagram Overview:**The Venn diagram illustrated consists of two overlapping circles labeled A and B. The overlap between these circles represents the elements common to both sets A and B.**Solution Steps:**1. Use the formula for the union of two sets: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]2. Substitute the known values into the equation: \[ 31 = 10 + 26 - n(A \cap B) \]3. Simplify to find \( n(A \cap B) \): \[ 31 = 36 - n(A \cap B) \]4. Solve for \( n(A \cap B) \): \[ n(A \cap B) = 36 - 31 = 5 \]**Conclusion:**The number of elements in the intersection of sets A and B, \( n(A \cap B) \), is 5.

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Answered: Qall 53% 6:24 B. X Suppose n(A) = 10,…

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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Qall 53% 6:24 B. X Suppose n(A) = 10, n(B) = 26, and n(A U B)=31. Use a Venn diagram to find n(An B). n(An B) = *** A