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Here are the meanings of some of the symbols that appear in the statements below E means "is a subset of." . C means "is a proper subset of." means "is not a subset of." is the empty set. For each statement, decide if it is true or false. ● ● Statement {t, u,y,z}cØ {1, 2, 3, 4, 5} {1, 3, 5} {c, g, j} C {c, d, f, g, h, j} {11, 14, 15, 19) ≤ (11, 14, 15, 19} True False O O O O

Here are the meanings of some of the symbols that appear in the statements below E means "is a subset of." . C means "is a proper subset of." means "is not a subset of." is the empty set. For each statement, decide if it is true or false. ● ● Statement {t, u,y,z}cØ {1, 2, 3, 4, 5} {1, 3, 5} {c, g, j} C {c, d, f, g, h, j} {11, 14, 15, 19) ≤ (11, 14, 15, 19} True False O O O O

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Identifying true statements involving subsets and proper subsets** --- Here are the meanings of some of the symbols that appear in the statements below: - \( \subseteq \) means "is a subset of." - \( \subset \) means "is a proper subset of." - \( \nsubseteq \) means "is not a subset of." - \( \emptyset \) is the empty set. For each statement, decide if it is true or false. | Statement | True | False | |:---|:---:|:---:| | \(\{t, u, y, z\} \subset \emptyset \) | ⬜ | ⬜ | | \(\{1, 2, 3, 4, 5\} \nsubseteq \{1, 3, 5\}\) | ⬜ | ⬜ | | \(\{c, g, j\} \subseteq \{c, d, f, g, h, j\}\) | ⬜ | ⬜ | | \(\{11, 14, 15, 19\} \subseteq \{11, 14, 15, 19\}\) | ⬜ | ⬜ | **Explanation** 1. **Statement:** \(\{t, u, y, z\} \subset \emptyset\) - **Analysis:** An empty set \((\emptyset)\) has no elements. Since \(\{t, u, y, z\}\) has elements, it cannot be a subset of the empty set. - **Conclusion:** False 2. **Statement:** \(\{1, 2, 3, 4, 5\} \nsubseteq \{1, 3, 5\}\) - **Analysis:** The set \(\{1, 2, 3, 4, 5\}\) contains elements \(2\) and \(4\) which are not in \(\{1, 3, 5\}\). Hence \(\{1, 2, 3, 4, 5\}\) is not a subset of \(\{1, 3, 5\}\). - **Conclusion:** True 3. **Statement:** \(\{c, g,
Transcribed Image Text:**Identifying true statements involving subsets and proper subsets** --- Here are the meanings of some of the symbols that appear in the statements below: - \( \subseteq \) means "is a subset of." - \( \subset \) means "is a proper subset of." - \( \nsubseteq \) means "is not a subset of." - \( \emptyset \) is the empty set. For each statement, decide if it is true or false. | Statement | True | False | |:---|:---:|:---:| | \(\{t, u, y, z\} \subset \emptyset \) | ⬜ | ⬜ | | \(\{1, 2, 3, 4, 5\} \nsubseteq \{1, 3, 5\}\) | ⬜ | ⬜ | | \(\{c, g, j\} \subseteq \{c, d, f, g, h, j\}\) | ⬜ | ⬜ | | \(\{11, 14, 15, 19\} \subseteq \{11, 14, 15, 19\}\) | ⬜ | ⬜ | **Explanation** 1. **Statement:** \(\{t, u, y, z\} \subset \emptyset\) - **Analysis:** An empty set \((\emptyset)\) has no elements. Since \(\{t, u, y, z\}\) has elements, it cannot be a subset of the empty set. - **Conclusion:** False 2. **Statement:** \(\{1, 2, 3, 4, 5\} \nsubseteq \{1, 3, 5\}\) - **Analysis:** The set \(\{1, 2, 3, 4, 5\}\) contains elements \(2\) and \(4\) which are not in \(\{1, 3, 5\}\). Hence \(\{1, 2, 3, 4, 5\}\) is not a subset of \(\{1, 3, 5\}\). - **Conclusion:** True 3. **Statement:** \(\{c, g,
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