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**Use the Venn diagram to determine the roster form of the indicated set:** (A ∪ C') Which is set (A ∪ C') in roster form? - O A. {10, 11, 12} - O B. {1, 2, 12} - O C. {9, 12} - O D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11} **Venn Diagram Explanation:** The Venn diagram consists of three intersecting circles labeled A, B, and C within a universal set U. The numbers within each area represent the elements that belong to each set or intersection of sets. - **Circle A** includes the numbers: 1, 2, 4, 5, 6, 7 - **Circle B** includes the numbers: 3, 4, 5, 8, 9 - **Circle C** includes the numbers: 4, 5, 10, 11 - **The Universal Set (U)** includes all numbers shown in the diagram: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 **Set C'** refers to the complement of set C, which includes all elements in the Universal Set U that are not in set C. These elements are: 1, 2, 3, 6, 7, 8, 9, 12. To find **A ∪ C'**, combine all elements from set A and set C' without duplication: Elements from set A: 1, 2, 4, 5, 6, 7 Elements from set C': 1, 2, 3, 6, 7, 8, 9, 12 The combined set (A ∪ C') is: {1, 2, 3, 4, 5, 6, 7, 8, 9, 12} Thus, the correct answer is not listed, but the combination is closest to option: - D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11}

**Use the Venn diagram to determine the roster form of the indicated set:** (A ∪ C') Which is set (A ∪ C') in roster form? - O A. {10, 11, 12} - O B. {1, 2, 12} - O C. {9, 12} - O D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11} **Venn Diagram Explanation:** The Venn diagram consists of three intersecting circles labeled A, B, and C within a universal set U. The numbers within each area represent the elements that belong to each set or intersection of sets. - **Circle A** includes the numbers: 1, 2, 4, 5, 6, 7 - **Circle B** includes the numbers: 3, 4, 5, 8, 9 - **Circle C** includes the numbers: 4, 5, 10, 11 - **The Universal Set (U)** includes all numbers shown in the diagram: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 **Set C'** refers to the complement of set C, which includes all elements in the Universal Set U that are not in set C. These elements are: 1, 2, 3, 6, 7, 8, 9, 12. To find **A ∪ C'**, combine all elements from set A and set C' without duplication: Elements from set A: 1, 2, 4, 5, 6, 7 Elements from set C': 1, 2, 3, 6, 7, 8, 9, 12 The combined set (A ∪ C') is: {1, 2, 3, 4, 5, 6, 7, 8, 9, 12} Thus, the correct answer is not listed, but the combination is closest to option: - D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11}

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Use the Venn diagram to determine the roster form of the indicated set:** (A ∪ C') Which is set (A ∪ C') in roster form? - O A. {10, 11, 12} - O B. {1, 2, 12} - O C. {9, 12} - O D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11} **Venn Diagram Explanation:** The Venn diagram consists of three intersecting circles labeled A, B, and C within a universal set U. The numbers within each area represent the elements that belong to each set or intersection of sets. - **Circle A** includes the numbers: 1, 2, 4, 5, 6, 7 - **Circle B** includes the numbers: 3, 4, 5, 8, 9 - **Circle C** includes the numbers: 4, 5, 10, 11 - **The Universal Set (U)** includes all numbers shown in the diagram: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 **Set C'** refers to the complement of set C, which includes all elements in the Universal Set U that are not in set C. These elements are: 1, 2, 3, 6, 7, 8, 9, 12. To find **A ∪ C'**, combine all elements from set A and set C' without duplication: Elements from set A: 1, 2, 4, 5, 6, 7 Elements from set C': 1, 2, 3, 6, 7, 8, 9, 12 The combined set (A ∪ C') is: {1, 2, 3, 4, 5, 6, 7, 8, 9, 12} Thus, the correct answer is not listed, but the combination is closest to option: - D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11}
Transcribed Image Text:**Use the Venn diagram to determine the roster form of the indicated set:** (A ∪ C') Which is set (A ∪ C') in roster form? - O A. {10, 11, 12} - O B. {1, 2, 12} - O C. {9, 12} - O D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11} **Venn Diagram Explanation:** The Venn diagram consists of three intersecting circles labeled A, B, and C within a universal set U. The numbers within each area represent the elements that belong to each set or intersection of sets. - **Circle A** includes the numbers: 1, 2, 4, 5, 6, 7 - **Circle B** includes the numbers: 3, 4, 5, 8, 9 - **Circle C** includes the numbers: 4, 5, 10, 11 - **The Universal Set (U)** includes all numbers shown in the diagram: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 **Set C'** refers to the complement of set C, which includes all elements in the Universal Set U that are not in set C. These elements are: 1, 2, 3, 6, 7, 8, 9, 12. To find **A ∪ C'**, combine all elements from set A and set C' without duplication: Elements from set A: 1, 2, 4, 5, 6, 7 Elements from set C': 1, 2, 3, 6, 7, 8, 9, 12 The combined set (A ∪ C') is: {1, 2, 3, 4, 5, 6, 7, 8, 9, 12} Thus, the correct answer is not listed, but the combination is closest to option: - D. {1, 2, 3, 4, 5, 6, 7, 8, 10, 11}
Expert Solution
Step 1

A Venn diagram is used to show the logical relations between a finite number of sets.

Union of sets (U) - It consists of all the elements in two sets.

i.e. Union of two set contains the elements belonging to either of the two sets.

 

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