Question 7 The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set. A 14 n(An B) = 6 3 9 B 9 minnenmath.com/assess2/?cid=184683&aid=13106154#/print 126 542 to 6 OSLO
Question 7 The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set. A 14 n(An B) = 6 3 9 B 9 minnenmath.com/assess2/?cid=184683&aid=13106154#/print 126 542 to 6 OSLO
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Question 7**
The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
The Venn diagram includes three circles labeled A, B, and C, that overlap with each other. The cardinalities of different regions within the circles are as follows:
- The cardinality of set A only (region not overlapping with B or C): 14
- The cardinality of set B only (region not overlapping with A or C): 7
- The cardinality of set C only (region not overlapping with A or B): 9
- The cardinality of the intersection of sets A and B only (not overlapping with C): 9
- The cardinality of the intersection of sets A and C only (not overlapping with B): 6
- The cardinality of the intersection of sets B and C only (not overlapping with A): 4
- The cardinality of the intersection of all three sets A, B, and C: 3
- The cardinality of the universal set outside of A, B, and C: 15
To find the cardinality of the set \( n(A \cap B^c) \), which represents the number of elements in set A that are not in set B, you add the cardinalities of the regions in set A excluding those in set B:
\[ n(A \cap B^c) = 14 + 6 \]
Therefore, the cardinality is:
\[ n(A \cap B^c) = 20 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2Fdc6ca996-6a33-40df-9471-c638fe2e3b19%2F05dw9l5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 7**
The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
The Venn diagram includes three circles labeled A, B, and C, that overlap with each other. The cardinalities of different regions within the circles are as follows:
- The cardinality of set A only (region not overlapping with B or C): 14
- The cardinality of set B only (region not overlapping with A or C): 7
- The cardinality of set C only (region not overlapping with A or B): 9
- The cardinality of the intersection of sets A and B only (not overlapping with C): 9
- The cardinality of the intersection of sets A and C only (not overlapping with B): 6
- The cardinality of the intersection of sets B and C only (not overlapping with A): 4
- The cardinality of the intersection of all three sets A, B, and C: 3
- The cardinality of the universal set outside of A, B, and C: 15
To find the cardinality of the set \( n(A \cap B^c) \), which represents the number of elements in set A that are not in set B, you add the cardinalities of the regions in set A excluding those in set B:
\[ n(A \cap B^c) = 14 + 6 \]
Therefore, the cardinality is:
\[ n(A \cap B^c) = 20 \]
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