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
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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![### 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 \( \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a4d37d3-cfd7-49ff-9170-60cb41cb998b%2F233af77a-f3b4-4380-92d5-4de651eb5628%2Fqpbl1tw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 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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