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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

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

Algebra and Trigonometry (6th Edition)
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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**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.
Transcribed Image Text:**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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