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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

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 22E: License Plate Numbers In a certain state, each automobile license plate number consists of two...
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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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