Sets B and C are subsets of the universal set U. These sets are defined as follows. U={1, 2, 5, 7, 8, 9) B = {1, 2, 7,9} C={8,9} Find the following sets. Write your answer in roster form or as Ø. (a) BUC' = (b) (Bnc)' = 0
Sets B and C are subsets of the universal set U. These sets are defined as follows. U={1, 2, 5, 7, 8, 9) B = {1, 2, 7,9} C={8,9} Find the following sets. Write your answer in roster form or as Ø. (a) BUC' = (b) (Bnc)' = 0
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 26E: Determine whether the set S={2x+x2,8+x3,x2+x3,4+x2} spans P3.
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![### Unions, Intersections, and Complements Involving 2 Sets
#### Sets \(\mathbf{B}\) and \(\mathbf{C}\) are subsets of the universal set \(\mathbf{U}\).
These sets are defined as follows:
\[
\mathbf{U} = \{1, 2, 5, 7, 8, 9\}
\]
\[
\mathbf{B} = \{1, 2, 7, 9\}
\]
\[
\mathbf{C} = \{8, 9\}
\]
#### Find the following sets. Write your answer in **roster form** or as \(\varnothing\).
1. **Union and Complement Operations (a):**
\[
\mathbf{B} \cup \mathbf{C^{\prime}} = \_\_\_\_\_
\]
2. **Intersection and Complement Operations (b):**
\[
(\mathbf{B} \cap \mathbf{C})^{\prime} = \_\_\_\_\_
\]
#### Explanation and Steps
1. **Step-by-Step for (a):**
- Identify \(\mathbf{C^{\prime}}\), the complement of \(\mathbf{C}\).
\[
\mathbf{C} = \{8, 9\}
\]
\[
\mathbf{U} = \{1, 2, 5, 7, 8, 9\}
\]
\[
\mathbf{C^{\prime}} = \mathbf{U} - \mathbf{C} = \{1, 2, 5, 7\}
\]
- Perform the union operation:
\[
\mathbf{B} = \{1, 2, 7, 9\}
\]
\[
\mathbf{C^{\prime}} = \{1, 2, 5, 7\}
\]
\[
\mathbf{B} \cup \mathbf{C^{\prime}} = \{1, 2, 5, 7, 9\}
\]
2. **Step-by-Step for (b):**
- Identify the intersection of \(\mathbf{B}\) and \(\mathbf{C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a4d37d3-cfd7-49ff-9170-60cb41cb998b%2Fad4b40d7-5f29-4d04-8e12-e6dd6f6eb510%2Frl1zl0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Unions, Intersections, and Complements Involving 2 Sets
#### Sets \(\mathbf{B}\) and \(\mathbf{C}\) are subsets of the universal set \(\mathbf{U}\).
These sets are defined as follows:
\[
\mathbf{U} = \{1, 2, 5, 7, 8, 9\}
\]
\[
\mathbf{B} = \{1, 2, 7, 9\}
\]
\[
\mathbf{C} = \{8, 9\}
\]
#### Find the following sets. Write your answer in **roster form** or as \(\varnothing\).
1. **Union and Complement Operations (a):**
\[
\mathbf{B} \cup \mathbf{C^{\prime}} = \_\_\_\_\_
\]
2. **Intersection and Complement Operations (b):**
\[
(\mathbf{B} \cap \mathbf{C})^{\prime} = \_\_\_\_\_
\]
#### Explanation and Steps
1. **Step-by-Step for (a):**
- Identify \(\mathbf{C^{\prime}}\), the complement of \(\mathbf{C}\).
\[
\mathbf{C} = \{8, 9\}
\]
\[
\mathbf{U} = \{1, 2, 5, 7, 8, 9\}
\]
\[
\mathbf{C^{\prime}} = \mathbf{U} - \mathbf{C} = \{1, 2, 5, 7\}
\]
- Perform the union operation:
\[
\mathbf{B} = \{1, 2, 7, 9\}
\]
\[
\mathbf{C^{\prime}} = \{1, 2, 5, 7\}
\]
\[
\mathbf{B} \cup \mathbf{C^{\prime}} = \{1, 2, 5, 7, 9\}
\]
2. **Step-by-Step for (b):**
- Identify the intersection of \(\mathbf{B}\) and \(\mathbf{C
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