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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 10 9 8 2 14 n(AUB) = 43 X 7 12 B

The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set. A 10 9 8 2 14 n(AUB) = 43 X 7 12 B

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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43 is not correct please help
**Understanding Venn Diagrams: An Educational Guide** ### Venn Diagram Analysis **Image Description:** The provided Venn diagram visually represents the cardinalities (number of elements) of three sets, A, B, and C. The sets are displayed as overlapping circles with corresponding numerical values indicating the number of elements in each section of the circles. **Key Elements:** - **Set A**: Represented by a blue circle. - **Set B**: Represented by a green circle. - **Set C**: Represented by a red circle. **Cardinalities (Number of Elements):** - **Only in A**: 10 - **Only in B**: 12 - **Only in C**: 14 - **A ∩ B** (only in both A and B): 8 - **A ∩ C** (only in both A and C): 9 - **B ∩ C** (only in both B and C): 7 - **A ∩ B ∩ C** (in A, B, and C): 2 ### Calculation of Union and Complement To find the cardinality of \( n(A \cup B^C) \) (i.e., the number of elements in the union of set A and the complement of set B): 1. **Elements in set A**: - Elements only in A: 10 - Elements in A and B: 8 - Elements in A, B, and C: 2 - Elements in A and C: 9 The total elements in A = 10 + 8 + 2 + 9 = 29 2. **Elements in the complement of B (\( B^C \))**: - Elements only in C: 14 - Elements only in A: 10 - Elements in A and C: 9 - Elements only in B are excluded. 3. **Combining A and \( B^C \)**: - All elements in A: 29 - Elements only in C: 14 - Elements in A and C: 9 (already included in A's total) 4. **Total Calculation**: - Total elements in \( A \cup B^C \) = Total (A) + (elements only in C) -
Transcribed Image Text:**Understanding Venn Diagrams: An Educational Guide** ### Venn Diagram Analysis **Image Description:** The provided Venn diagram visually represents the cardinalities (number of elements) of three sets, A, B, and C. The sets are displayed as overlapping circles with corresponding numerical values indicating the number of elements in each section of the circles. **Key Elements:** - **Set A**: Represented by a blue circle. - **Set B**: Represented by a green circle. - **Set C**: Represented by a red circle. **Cardinalities (Number of Elements):** - **Only in A**: 10 - **Only in B**: 12 - **Only in C**: 14 - **A ∩ B** (only in both A and B): 8 - **A ∩ C** (only in both A and C): 9 - **B ∩ C** (only in both B and C): 7 - **A ∩ B ∩ C** (in A, B, and C): 2 ### Calculation of Union and Complement To find the cardinality of \( n(A \cup B^C) \) (i.e., the number of elements in the union of set A and the complement of set B): 1. **Elements in set A**: - Elements only in A: 10 - Elements in A and B: 8 - Elements in A, B, and C: 2 - Elements in A and C: 9 The total elements in A = 10 + 8 + 2 + 9 = 29 2. **Elements in the complement of B (\( B^C \))**: - Elements only in C: 14 - Elements only in A: 10 - Elements in A and C: 9 - Elements only in B are excluded. 3. **Combining A and \( B^C \)**: - All elements in A: 29 - Elements only in C: 14 - Elements in A and C: 9 (already included in A's total) 4. **Total Calculation**: - Total elements in \( A \cup B^C \) = Total (A) + (elements only in C) -
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