### Union of Sets: Understanding through Venn Diagrams#### Example Problem**Problem Statement:**Let $ U $ be the set of integers from 1 to 15:\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} \]Set $ A $ and set $ B $ are subsets of $ U $. Set $ A $ contains multiples of 2, such as 2, 4, 6, ..., while Set $ B $ contains multiples of 3, such as 3, 6, 9, ...#### Venn Diagram and Union of SetsUse the Venn diagram below to help answer the question. The diagram illustrates the relationship between sets $ A $ and $ B $ within the universal set $ U $.**Venn Diagram Explanation:**- The Venn diagram contains two intersecting circles within a rectangle. - The rectangle represents the universal set $ U $.- Circle $ A $ represents multiples of 2.- Circle $ B $ represents multiples of 3.- The intersection of circles $ A $ and $ B $ represents the elements that are multiples of both 2 and 3.#### Question:Which set is $ A \cup B $ (the union of sets $ A $ and $ B $)?- $ \{1, 3, 5, 7, 9, 11, 13, 15\} $- $ \{1, 2, 4, 5, 7, 8, 10, 11, 13, 14\} $- $ \{6, 12\} $- $ \{2, 3, 4, 6, 8, 9, 10, 12, 14, 15\} $The correct answer is the option that lists all unique elements that are in either set $ A $, set $ B $, or both.

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Description: ### Union of Sets: Understanding through Venn Diagrams#### Example Problem**Problem Statement:**Let $ U $ be the set of integers from 1 to 15:\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} \]Set $ A $ and set $ B $ are subsets of

Union of the two sets is a set containing all elements that are in A or in B.

Math

Algebra

Let U be the set of integers from 1 to 15. U = {1,2,3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} Set A and set B are subsets of U. Set A contains multiples of 2, such as 2, 4, 6.... Set B contains multiples of 3, such as 3, 6, 9.... Use the Venn diagram to help answer the question. A Multiples of 2 B Multiples of 3 U © 2020 StrongMind. Created using GeoGebra. Which set is AU B? O {1,3, 5, 7,9, 11, 13, 15} O {1,2, 4, 5, 7, 8, 10, 11, 13, 14} O {6, 12} O {2,3, 4, 6, 8, 9, 10, 12, 14, 15}

Let U be the set of integers from 1 to 15. U = {1,2,3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} Set A and set B are subsets of U. Set A contains multiples of 2, such as 2, 4, 6.... Set B contains multiples of 3, such as 3, 6, 9.... Use the Venn diagram to help answer the question. A Multiples of 2 B Multiples of 3 U © 2020 StrongMind. Created using GeoGebra. Which set is AU B? O {1,3, 5, 7,9, 11, 13, 15} O {1,2, 4, 5, 7, 8, 10, 11, 13, 14} O {6, 12} O {2,3, 4, 6, 8, 9, 10, 12, 14, 15}

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Union of Sets: Understanding through Venn Diagrams

#### Example Problem

**Problem Statement:**

Let $ U $ be the set of integers from 1 to 15:

\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\} \]

Set $ A $ and set $ B $ are subsets of $ U $. Set $ A $ contains multiples of 2, such as 2, 4, 6, ..., while Set $ B $ contains multiples of 3, such as 3, 6, 9, ...

#### Venn Diagram and Union of Sets

Use the Venn diagram below to help answer the question. The diagram illustrates the relationship between sets $ A $ and $ B $ within the universal set $ U $.

**Venn Diagram Explanation:**

- The Venn diagram contains two intersecting circles within a rectangle.
- The rectangle represents the universal set $ U $.
- Circle $ A $ represents multiples of 2.
- Circle $ B $ represents multiples of 3.
- The intersection of circles $ A $ and $ B $ represents the elements that are multiples of both 2 and 3.

<img src="https://i.imgur.com/ZSl0p4i.png" alt="Venn Diagram">

#### Question:

Which set is $ A \cup B $ (the union of sets $ A $ and $ B $)?

- $ \{1, 3, 5, 7, 9, 11, 13, 15\} $
- $ \{1, 2, 4, 5, 7, 8, 10, 11, 13, 14\} $
- $ \{6, 12\} $
- $ \{2, 3, 4, 6, 8, 9, 10, 12, 14, 15\} $

The correct answer is the option that lists all unique elements that are in either set $ A $, set $ B $, or both.

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