Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.
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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![### Mathematical Expression Validation
Let \( A \), \( B \), \( C \), \( D \) be sets.
The expression given is:
\[ (A \cap B) \times (C \cap D) = (A \times C) \cap (B \times D) \]
**Question:** Is the above expression true or false?
- ○ True.
- ○ False.
**Explanation:**
The left-hand side of the equation \((A \cap B) \times (C \cap D)\) represents the Cartesian product of the intersection of sets \(A\) and \(B\) with the intersection of sets \(C\) and \(D\).
The right-hand side \((A \times C) \cap (B \times D)\) represents the intersection of the Cartesian product of sets \(A\) and \(C\) with the Cartesian product of sets \(B\) and \(D\).
To verify the equality, one would need to explore the properties of Cartesian products and intersections of sets thoroughly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd76a2d57-02e6-4734-ba8a-6fadc8c476a5%2F6fcb0673-26c5-406c-af2a-29f9f4afb450%2Fqaaj05d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Mathematical Expression Validation
Let \( A \), \( B \), \( C \), \( D \) be sets.
The expression given is:
\[ (A \cap B) \times (C \cap D) = (A \times C) \cap (B \times D) \]
**Question:** Is the above expression true or false?
- ○ True.
- ○ False.
**Explanation:**
The left-hand side of the equation \((A \cap B) \times (C \cap D)\) represents the Cartesian product of the intersection of sets \(A\) and \(B\) with the intersection of sets \(C\) and \(D\).
The right-hand side \((A \times C) \cap (B \times D)\) represents the intersection of the Cartesian product of sets \(A\) and \(C\) with the Cartesian product of sets \(B\) and \(D\).
To verify the equality, one would need to explore the properties of Cartesian products and intersections of sets thoroughly.
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