**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:** False2. **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:** True3. **Statement:** \(\{c, g,

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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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Question

**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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