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The Venn diagram here shows the cardinality of each set. Use this to find the car given set. 0630 Oneariou A 12 с 6 n(AU (BNC)) = 8 1 6 5 8 B 3 209(GLUGU: 201930) 18:10)

The Venn diagram here shows the cardinality of each set. Use this to find the car given set. 0630 Oneariou A 12 с 6 n(AU (BNC)) = 8 1 6 5 8 B 3 209(GLUGU: 201930) 18:10)

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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### Question 10 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 overlapping circles labeled A, B, and C. Here's a detailed explanation of the diagram: - **Circle A** (on the left side): - Contains the number 12 (exclusive to A) - Shares the number 8 with circle B - Shares the numbers 6 and 1 with circle C - **Circle B** (on the right side): - Contains the number 8 (exclusive to B) - Shares the number 8 with circle A - Shares the numbers 5 and 1 with circle C - **Circle C** (at the bottom): - Contains the number 6 (exclusive to C) - Shares the numbers 6 and 1 with circle A - Shares the numbers 5 and 1 with circle B - **Intersection of all three circles (A, B, and C)**: - Contains the number 1 Below the Venn diagram, the problem asks to find the cardinality of the set \( n(A \cup (B \cap C)) \). **Solution:** To find the cardinality of \( n(A \cup (B \cap C)) \), you need to identify all elements that are in set A or in the intersection of sets B and C. **\((B \cap C)\)** contains the numbers that are common in both B and C, which are: - 1, 5 Thus, **\((A \cup (B \cap C))\)** will include all elements in set A and all elements in the intersection of B and C, without double-counting any elements. - From A: 12, 8, 6, 1 - From B ∩ C: 1, 5 Combining these without double-counting the number 1, the elements in \( A \cup (B \cap C) \) are: - 12, 8, 6, 1, 5 Thus, the cardinality \( n(A \cup (B \cap C)) \) is the total number of unique elements in this set, which is: \[ n(A \cup (B \cap C)) = 5 \ So, the answer is
Transcribed Image Text:### Question 10 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 overlapping circles labeled A, B, and C. Here's a detailed explanation of the diagram: - **Circle A** (on the left side): - Contains the number 12 (exclusive to A) - Shares the number 8 with circle B - Shares the numbers 6 and 1 with circle C - **Circle B** (on the right side): - Contains the number 8 (exclusive to B) - Shares the number 8 with circle A - Shares the numbers 5 and 1 with circle C - **Circle C** (at the bottom): - Contains the number 6 (exclusive to C) - Shares the numbers 6 and 1 with circle A - Shares the numbers 5 and 1 with circle B - **Intersection of all three circles (A, B, and C)**: - Contains the number 1 Below the Venn diagram, the problem asks to find the cardinality of the set \( n(A \cup (B \cap C)) \). **Solution:** To find the cardinality of \( n(A \cup (B \cap C)) \), you need to identify all elements that are in set A or in the intersection of sets B and C. **\((B \cap C)\)** contains the numbers that are common in both B and C, which are: - 1, 5 Thus, **\((A \cup (B \cap C))\)** will include all elements in set A and all elements in the intersection of B and C, without double-counting any elements. - From A: 12, 8, 6, 1 - From B ∩ C: 1, 5 Combining these without double-counting the number 1, the elements in \( A \cup (B \cap C) \) are: - 12, 8, 6, 1, 5 Thus, the cardinality \( n(A \cup (B \cap C)) \) is the total number of unique elements in this set, which is: \[ n(A \cup (B \cap C)) = 5 \ So, the answer is
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