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The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set. A n (An BnCc) = 9 11 B 8

The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set. A n (An BnCc) = 9 11 B 8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Educational Content: Venn Diagram Analysis** The Venn diagram illustrates the cardinality of three sets: A, B, and C. Each circle represents a set, and the numbers inside denote the number of elements in each specific region of the diagram. - **Set A** (Blue Circle): - Elements unique to A: 5 - Elements shared with B only: 7 - Elements shared with C only: 6 - Elements shared with both B and C: 2 - **Set B** (Green Circle): - Elements unique to B: 11 - Elements shared with A only: 7 - Elements shared with C only: 9 - Elements shared with both A and C: 2 - **Set C** (Red Circle): - Elements unique to C: 9 - Elements shared with A only: 6 - Elements shared with B only: 9 - Elements shared with both A and B: 2 **Additional Information:** - There is an 8, which represents the exterior of the diagram, indicating elements not belonging to any of the sets A, B, or C. **Objective:** Find the cardinality of the intersection of sets A and B, excluding elements from set C, represented as \( n(A \cap B \cap C^c) \). - **Solution:** The region representing \( n(A \cap B \cap C^c) \) is 7. This analysis helps in understanding the relationships and intersections between the sets.
Transcribed Image Text:**Educational Content: Venn Diagram Analysis** The Venn diagram illustrates the cardinality of three sets: A, B, and C. Each circle represents a set, and the numbers inside denote the number of elements in each specific region of the diagram. - **Set A** (Blue Circle): - Elements unique to A: 5 - Elements shared with B only: 7 - Elements shared with C only: 6 - Elements shared with both B and C: 2 - **Set B** (Green Circle): - Elements unique to B: 11 - Elements shared with A only: 7 - Elements shared with C only: 9 - Elements shared with both A and C: 2 - **Set C** (Red Circle): - Elements unique to C: 9 - Elements shared with A only: 6 - Elements shared with B only: 9 - Elements shared with both A and B: 2 **Additional Information:** - There is an 8, which represents the exterior of the diagram, indicating elements not belonging to any of the sets A, B, or C. **Objective:** Find the cardinality of the intersection of sets A and B, excluding elements from set C, represented as \( n(A \cap B \cap C^c) \). - **Solution:** The region representing \( n(A \cap B \cap C^c) \) is 7. This analysis helps in understanding the relationships and intersections between the sets.
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