Write down the following sets explicitly. (a) P({0}) (b) {Ø, {0}} × {2, 3, 5}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Title: Understanding Set Operations**
**Problem: Write Down the Following Sets Explicitly**
(a) \( P(\{\emptyset\}) \)
- **Explanation**: The power set of any set is the set of all its subsets. For the set \(\{\emptyset\}\), the subsets are:
- The empty set: \(\emptyset\)
- The set itself: \(\{\emptyset\}\)
Therefore, the power set is:
\[
P(\{\emptyset\}) = \{\emptyset, \{\emptyset\}\}
\]
(b) \(\{\emptyset, \{\emptyset\}\} \times \{2, 3, 5\}\)
- **Explanation**: The Cartesian product of two sets involves pairing each element of the first set with each element of the second set. For the sets \(\{\emptyset, \{\emptyset\}\}\) and \(\{2, 3, 5\}\), the Cartesian product is as follows:
- Pair \(\emptyset\) with each element of \(\{2, 3, 5\}\):
- \((\emptyset, 2)\)
- \((\emptyset, 3)\)
- \((\emptyset, 5)\)
- Pair \(\{\emptyset\}\) with each element of \(\{2, 3, 5\}\):
- \((\{\emptyset\}, 2)\)
- \((\{\emptyset\}, 3)\)
- \((\{\emptyset\}, 5)\)
Thus, the Cartesian product is:
\[
\{\emptyset, \{\emptyset\}\} \times \{2, 3, 5\} = \{(\emptyset, 2), (\emptyset, 3), (\emptyset, 5), (\{\emptyset\}, 2), (\{\emptyset\}, 3), (\{\emptyset\}, 5)\}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F382d69cf-ffe2-43c0-99c4-21bedf550518%2F779b09e0-56fb-4fb0-882f-d0151d100799%2Fv395x1b_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Set Operations**
**Problem: Write Down the Following Sets Explicitly**
(a) \( P(\{\emptyset\}) \)
- **Explanation**: The power set of any set is the set of all its subsets. For the set \(\{\emptyset\}\), the subsets are:
- The empty set: \(\emptyset\)
- The set itself: \(\{\emptyset\}\)
Therefore, the power set is:
\[
P(\{\emptyset\}) = \{\emptyset, \{\emptyset\}\}
\]
(b) \(\{\emptyset, \{\emptyset\}\} \times \{2, 3, 5\}\)
- **Explanation**: The Cartesian product of two sets involves pairing each element of the first set with each element of the second set. For the sets \(\{\emptyset, \{\emptyset\}\}\) and \(\{2, 3, 5\}\), the Cartesian product is as follows:
- Pair \(\emptyset\) with each element of \(\{2, 3, 5\}\):
- \((\emptyset, 2)\)
- \((\emptyset, 3)\)
- \((\emptyset, 5)\)
- Pair \(\{\emptyset\}\) with each element of \(\{2, 3, 5\}\):
- \((\{\emptyset\}, 2)\)
- \((\{\emptyset\}, 3)\)
- \((\{\emptyset\}, 5)\)
Thus, the Cartesian product is:
\[
\{\emptyset, \{\emptyset\}\} \times \{2, 3, 5\} = \{(\emptyset, 2), (\emptyset, 3), (\emptyset, 5), (\{\emptyset\}, 2), (\{\emptyset\}, 3), (\{\emptyset\}, 5)\}
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
