Let be a family of sets and let B E . Prove that BC UAE A. Proof. Let E B. Define A = [Select] so that it guarantees that A € and also a EA. As we have chosen A particularly, * EA for [Select] AE. By definition of the union of family of sets, [Select] BCUAE A. V E UAE A. Hence
Let be a family of sets and let B E . Prove that BC UAE A. Proof. Let E B. Define A = [Select] so that it guarantees that A € and also a EA. As we have chosen A particularly, * EA for [Select] AE. By definition of the union of family of sets, [Select] BCUAE A. V E UAE A. Hence
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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![**Let \( \mathcal{A} \) be a family of sets and let \( B \in \mathcal{A} \). Prove that \( B \subseteq \bigcup_{A \in \mathcal{A}} A \).**
**Proof.** Let \( x \in B \). Define \( A = [\text{Select}] \) so that it guarantees that \( A \in \mathcal{A} \) and also \( x \in A \). As we have chosen \( A \) particularly, \( x \in A \) for \( [\text{Select}] \) \( A \in \mathcal{A} \). By definition of the union of family of sets, \( [\text{Select}] \in \bigcup_{A \in \mathcal{A}} A \). Hence \( B \subseteq \bigcup_{A \in \mathcal{A}} A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9b346ae-ef24-4d99-babf-e95763a360cd%2Fa52d77e3-e3a6-4d3a-8bda-0181a8423903%2F4vfo43h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Let \( \mathcal{A} \) be a family of sets and let \( B \in \mathcal{A} \). Prove that \( B \subseteq \bigcup_{A \in \mathcal{A}} A \).**
**Proof.** Let \( x \in B \). Define \( A = [\text{Select}] \) so that it guarantees that \( A \in \mathcal{A} \) and also \( x \in A \). As we have chosen \( A \) particularly, \( x \in A \) for \( [\text{Select}] \) \( A \in \mathcal{A} \). By definition of the union of family of sets, \( [\text{Select}] \in \bigcup_{A \in \mathcal{A}} A \). Hence \( B \subseteq \bigcup_{A \in \mathcal{A}} A \).
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