MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Educational Content: Union of Sets** --- **Problem Statement:** Given the following sets: - \( U = \{0, 1, 2, 3, 4, 5, \dots\} \) - \( C = \{1, 2, 3, 4, \dots\} \) - \( D = \{4, 8, 12, 16, \dots\} \) Determine the set \( C \cup D \). --- **Union of Sets Explanation:** The union of two sets, \( C \cup D \), is the set containing all elements that are in \( C \), in \( D \), or in both. 1. **Set \( C \)** is given as \( \{1, 2, 3, 4, \dots\} \). - This represents all positive integers. 2. **Set \( D \)** is given as \( \{4, 8, 12, 16, \dots\} \). - This represents the multiples of 4. **Steps to find \( C \cup D \):** - List out the elements of both sets. - Combine the elements into a single set, ensuring no duplicates. ### Solution: - Elements of \( C \) = \( \{1, 2, 3, 4, 5, 6, 7, 8, 9, \dots\} \) (all positive integers) - Elements of \( D \) = \( \{4, 8, 12, 16, \dots\} \) (multiples of 4) Combining these: \[C \cup D = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, \dots\} \] Thus, \(C \cup D\) is the set of all positive integers, as any multiple of 4 is already included in the positive integers. --- **Multiple Choice Question:** Choose the correct answer below: - **A.** \( C \cup D = \{1, 2, 3, 4, \dots\} \) - **B.** \( C \cup D = \{4, 8, 12, 16
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Transcribed Image Text:**Educational Content: Union of Sets** --- **Problem Statement:** Given the following sets: - \( U = \{0, 1, 2, 3, 4, 5, \dots\} \) - \( C = \{1, 2, 3, 4, \dots\} \) - \( D = \{4, 8, 12, 16, \dots\} \) Determine the set \( C \cup D \). --- **Union of Sets Explanation:** The union of two sets, \( C \cup D \), is the set containing all elements that are in \( C \), in \( D \), or in both. 1. **Set \( C \)** is given as \( \{1, 2, 3, 4, \dots\} \). - This represents all positive integers. 2. **Set \( D \)** is given as \( \{4, 8, 12, 16, \dots\} \). - This represents the multiples of 4. **Steps to find \( C \cup D \):** - List out the elements of both sets. - Combine the elements into a single set, ensuring no duplicates. ### Solution: - Elements of \( C \) = \( \{1, 2, 3, 4, 5, 6, 7, 8, 9, \dots\} \) (all positive integers) - Elements of \( D \) = \( \{4, 8, 12, 16, \dots\} \) (multiples of 4) Combining these: \[C \cup D = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, \dots\} \] Thus, \(C \cup D\) is the set of all positive integers, as any multiple of 4 is already included in the positive integers. --- **Multiple Choice Question:** Choose the correct answer below: - **A.** \( C \cup D = \{1, 2, 3, 4, \dots\} \) - **B.** \( C \cup D = \{4, 8, 12, 16
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