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Here are the meanings of some of the symbols that appear in the statements below. • 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 {12, 13, 15} {11, 12, 13, 14, 15} {1, 4, 5} Ø {c, d, f, g} C {d, f {r, t, y, z) Z {r, t, y, z) True False O O O O O O X

Here are the meanings of some of the symbols that appear in the statements below. • 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 {12, 13, 15} {11, 12, 13, 14, 15} {1, 4, 5} Ø {c, d, f, g} C {d, f {r, t, y, z) Z {r, t, y, z) True False O 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 ## Understanding Symbols: 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. ## Instructions: For each statement, decide if it is true or false. ### Statements: 1. \(\{12, 13, 15\} \subseteq \{11, 12, 13, 14, 15\}\) - True \( \bigcirc \) - False \( \phantom{\bigcirc} \) 2. \(\{1, 4, 5\} \subseteq \emptyset\) - True \( \phantom{\bigcirc} \) - False \( \bigcirc \) 3. \(\{c, d, f, g\} \subset \{d, f\}\) - True \( \phantom{\bigcirc} \) - False \( \bigcirc \) 4. \(\{r, t, y, z\} \nsubseteq \{r, t, y, z\}\) - True \( \phantom{\bigcirc} \) - False \( \bigcirc \) ### Additional Features: - **Explanation Button:** Clicking this button may provide explanations for each statement. - **Check Button:** Clicking this button may check the answers and provide feedback. This exercise helps you understand and identify subsets and proper subsets in set theory, a fundamental aspect of mathematics.
Transcribed Image Text:# Identifying True Statements Involving Subsets and Proper Subsets ## Understanding Symbols: 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. ## Instructions: For each statement, decide if it is true or false. ### Statements: 1. \(\{12, 13, 15\} \subseteq \{11, 12, 13, 14, 15\}\) - True \( \bigcirc \) - False \( \phantom{\bigcirc} \) 2. \(\{1, 4, 5\} \subseteq \emptyset\) - True \( \phantom{\bigcirc} \) - False \( \bigcirc \) 3. \(\{c, d, f, g\} \subset \{d, f\}\) - True \( \phantom{\bigcirc} \) - False \( \bigcirc \) 4. \(\{r, t, y, z\} \nsubseteq \{r, t, y, z\}\) - True \( \phantom{\bigcirc} \) - False \( \bigcirc \) ### Additional Features: - **Explanation Button:** Clicking this button may provide explanations for each statement. - **Check Button:** Clicking this button may check the answers and provide feedback. This exercise helps you understand and identify subsets and proper subsets in set theory, a fundamental aspect of mathematics.
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