Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:### Identifying True Statements Involving Subsets and Proper Subsets
In this section, we will learn to identify true statements involving subsets and proper subsets. Below are some symbol meanings that will help you understand the statements:
- \(\subseteq\) means "is a subset of."
- \(\subset\) means "is a proper subset of."
- \(\nsupseteq\) means "is not a subset of."
- \(\emptyset\) is the empty set.
For each statement, decide if it is true or false.
#### Statements
| Statement | True | False |
|---------------------------------------------------------------|------|-------|
| \(\{d, j, k, n\} \nsupseteq \{d, j, k, n\}\) | | X |
| \(\{1, 4\} \subseteq \{1, 2, 3, 4, \ldots\}\) | X | |
| \(\{p, q, r, s, t, u\} \subset \{p, r, u\}\) | | X |
| \(\emptyset \subset \{11, 12, 16, 19\}\) | X | |
Buttons are provided to select "True" or "False" for each statement.
**Explanation of the Statements:**
1. **Statement:** \(\{d, j, k, n\} \nsupseteq \{d, j, k, n\}\)
- This statement claims that the set \(\{d, j, k, n\}\) is not a subset of itself. This is false because any set is a subset of itself.
2. **Statement:** \(\{1, 4\} \subseteq \{1, 2, 3, 4, \ldots\}\)
- This statement claims that the set \(\{1, 4\}\) is a subset of the set \(\{1, 2, 3, 4, \ldots\}\). This is true because all elements of \(\{1, 4\}\) are in the larger set \(\{1, 2, 3, 4, \ldots\}\).
3. **
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