А 3D {1,3,5}, В 3 {2, 3} Check ALL of the following Cartesian products to which the following elements belong:
А 3D {1,3,5}, В 3 {2, 3} Check ALL of the following Cartesian products to which the following elements belong:
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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Transcribed Image Text:The image displays a multiple-choice question related to the Cartesian product of sets, with the following options:
(d) \((3, 3)\)
- □ A. \( B \times B \)
- □ B. \( B \times A \)
- □ C. \( A \times A \)
- ☑ D. \( A \times B \)
The correct answer, option D: \( A \times B \), is highlighted with a check mark.
![**Sets and Cartesian Products**
Given:
- \( A = \{1, 3, 5\} \)
- \( B = \{2, 3\} \)
**Task:**
Determine to which of the following Cartesian products the given elements belong.
**Understanding Cartesian Products:**
The Cartesian product of two sets \( A \) and \( B \), denoted \( A \times B \), is the set of all possible ordered pairs where the first element is from set \( A \) and the second is from set \( B \).
**Example for \( A \) and \( B \):**
\[ A \times B = \{(1, 2), (1, 3), (3, 2), (3, 3), (5, 2), (5, 3)\} \]
Each element needs to be evaluated to see which Cartesian product it belongs to, of the options provided (if given in a larger context).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb64c1c6f-d4d7-4d8b-8ebe-5eadb49feddc%2Ffd16ac43-8416-4e44-8370-f6d011cb9651%2Fe7yjic_processed.png&w=3840&q=75)
Transcribed Image Text:**Sets and Cartesian Products**
Given:
- \( A = \{1, 3, 5\} \)
- \( B = \{2, 3\} \)
**Task:**
Determine to which of the following Cartesian products the given elements belong.
**Understanding Cartesian Products:**
The Cartesian product of two sets \( A \) and \( B \), denoted \( A \times B \), is the set of all possible ordered pairs where the first element is from set \( A \) and the second is from set \( B \).
**Example for \( A \) and \( B \):**
\[ A \times B = \{(1, 2), (1, 3), (3, 2), (3, 3), (5, 2), (5, 3)\} \]
Each element needs to be evaluated to see which Cartesian product it belongs to, of the options provided (if given in a larger context).
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