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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 {1, 2, 3, 4, 5} {2, 4, 5} { {11, 14, 16} % 11, 12, 13, 14, 15, 16, } {d, f, g, k} ZO (21, 23, 24, 25, 29} C {21, 23, 24, 25, 293 ... True False O O O O O X

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 {1, 2, 3, 4, 5} {2, 4, 5} { {11, 14, 16} % 11, 12, 13, 14, 15, 16, } {d, f, g, k} ZO (21, 23, 24, 25, 29} C {21, 23, 24, 25, 293 ... True False O O O O O X

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 | |-------------------------------------------------------|------|-------| | \(\{1, 2, 3, 4, 5\} \subseteq \{2, 4, 5\}\) | | X | | \(\{11, 14, 16\} \subset \{11, 12, 13, 14, 15, 16\}\) | X | | | \(\{d, f, g, k\} \nsubseteq \emptyset\) | X | | | \(\{21, 23, 24, 25, 29\} \subset \{21, 23, 24, 25, 29\}\) | | X | Explanation for the entries: 1. \(\{1, 2, 3, 4, 5\} \subseteq \{2, 4, 5\}\): This statement is **false** because \(\{1, 2, 3, 4, 5\}\) contains elements not present in \(\{2, 4, 5\}\). 2. \(\{11, 14, 16\} \subset \{11, 12, 13, 14, 15, 16\}\): This statement is **true** because \(\{11, 14, 16\}\) is a proper subset of \(\{11, 12, 13, 14, 15, 16\}\), meaning all elements of the former set exist in the latter, and the latter contains additional elements. 3. \(\{d, f, g, k\} \nsubseteq \emptyset\): This statement is **true** because no non-empty set can be a subset of the empty
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 | |-------------------------------------------------------|------|-------| | \(\{1, 2, 3, 4, 5\} \subseteq \{2, 4, 5\}\) | | X | | \(\{11, 14, 16\} \subset \{11, 12, 13, 14, 15, 16\}\) | X | | | \(\{d, f, g, k\} \nsubseteq \emptyset\) | X | | | \(\{21, 23, 24, 25, 29\} \subset \{21, 23, 24, 25, 29\}\) | | X | Explanation for the entries: 1. \(\{1, 2, 3, 4, 5\} \subseteq \{2, 4, 5\}\): This statement is **false** because \(\{1, 2, 3, 4, 5\}\) contains elements not present in \(\{2, 4, 5\}\). 2. \(\{11, 14, 16\} \subset \{11, 12, 13, 14, 15, 16\}\): This statement is **true** because \(\{11, 14, 16\}\) is a proper subset of \(\{11, 12, 13, 14, 15, 16\}\), meaning all elements of the former set exist in the latter, and the latter contains additional elements. 3. \(\{d, f, g, k\} \nsubseteq \emptyset\): This statement is **true** because no non-empty set can be a subset of the empty
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