Show that for every pair of sets X and Y, the sets X × Y and U {(x, y) | y ≤ Y} xEX are equal.
Show that for every pair of sets X and Y, the sets X × Y and U {(x, y) | y ≤ Y} xEX are equal.
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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![**Problem Statement:**
Show that for every pair of sets \( X \) and \( Y \), the sets \( X \times Y \) and
\[
\bigcup_{x \in X} \{(x, y) \mid y \in Y\}
\]
are equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae6b9fe6-ccb1-44ed-9ed3-da8ae4f1d20a%2Fbc78d4e8-0aad-4a11-b3c0-8c18bdc66849%2Fayqk436_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Show that for every pair of sets \( X \) and \( Y \), the sets \( X \times Y \) and
\[
\bigcup_{x \in X} \{(x, y) \mid y \in Y\}
\]
are equal.
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