### Identifying True Statements Involving Subsets and Proper SubsetsThis section provides an understanding of various symbols used in statements about subsets and proper subsets. Here are the meanings of some of the symbols that you might encounter:- \( \subseteq \) 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:\[\begin{array}{|c|c|c|}\hline\text{Statement} & \text{True} & \text{False} \\\hline\{11, 14\} \nsubseteq \{11, 12, 13, 14, 15\} & \bigcirc & \bigcirc \\\hline\emptyset \subseteq \{3, 5, 8, 9\} & \bigcirc & \bigcirc \\\hline\{c, d, f, g\} \subseteq \{d, g\} & \bigcirc & \bigcirc \\\hline\{p, q, t, v, w\} \subseteq \{p, q, t, v, w\} & \bigcirc & \bigcirc \\\hline\end{array}\]**Explanation:** - The statement \( \{11, 14\} \nsubseteq \{11, 12, 13, 14, 15\} \) indicates that the set \{11, 14\} is not a subset of \{11, 12, 13, 14, 15\}. - The statement \( \emptyset \subseteq \{3, 5, 8, 9\} \) is asking whether the empty set is a subset of the set \{3, 5, 8, 9\}. - The statement \( \{c, d, f, g\} \subseteq \{d, g\} \) asks if \{c, d, f, g\} is a subset of \{d, g\}.- The statement \( \

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Statement {11, 14} {11, 12, 13, 14, 15} Ø (3, 5, 8, 9} {c, d, f, g} {d, g} (p, q, t, v, y) C(p, q, t, v, y} True False

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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Question

### Identifying True Statements Involving Subsets and Proper Subsets

This section provides an understanding of various symbols used in statements about subsets and proper subsets. Here are the meanings of some of the symbols that you might encounter:

- \( \subseteq \) 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:

\[
\begin{array}{|c|c|c|}
\hline
\text{Statement} & \text{True} & \text{False} \\
\hline
\{11, 14\} \nsubseteq \{11, 12, 13, 14, 15\} & \bigcirc & \bigcirc \\
\hline
\emptyset \subseteq \{3, 5, 8, 9\} & \bigcirc & \bigcirc \\
\hline
\{c, d, f, g\} \subseteq \{d, g\} & \bigcirc & \bigcirc \\
\hline
\{p, q, t, v, w\} \subseteq \{p, q, t, v, w\} & \bigcirc & \bigcirc \\
\hline
\end{array}
\]

**Explanation:**
- The statement \( \{11, 14\} \nsubseteq \{11, 12, 13, 14, 15\} \) indicates that the set \{11, 14\} is not a subset of \{11, 12, 13, 14, 15\}.
- The statement \( \emptyset \subseteq \{3, 5, 8, 9\} \) is asking whether the empty set is a subset of the set \{3, 5, 8, 9\}.
- The statement \( \{c, d, f, g\} \subseteq \{d, g\} \) asks if \{c, d, f, g\} is a subset of \{d, g\}.
- The statement \( \

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