Claim: Consider a family = {A i EN} of sets such that A1 CA2 CCA20 C..., then U20₁ Ai = A20. i=1 Proof. Since the union of the family contains every set in the family as a subset, we have A20 CU Ai. Next, let x E U₂₁ A₁. Then x € A; for [Select] But A CA20 for [Select] [Select] Hence U2₁A = A20. i=1,2,..., 20, so € A20. Thus UA C A 20. 20 i=1 i=1,2,..., 20.
Claim: Consider a family = {A i EN} of sets such that A1 CA2 CCA20 C..., then U20₁ Ai = A20. i=1 Proof. Since the union of the family contains every set in the family as a subset, we have A20 CU Ai. Next, let x E U₂₁ A₁. Then x € A; for [Select] But A CA20 for [Select] [Select] Hence U2₁A = A20. i=1,2,..., 20, so € A20. Thus UA C A 20. 20 i=1 i=1,2,..., 20.
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
First choice: Some or All
Second choice: Some or All
Third choice: i x or 20
![Claim: Consider a family = {A i EN} of sets such that
A1 CA2 CCA20 C..., then U20₁ Ai = A20.
i=1
Proof. Since the union of the family contains every set in the family as a subset, we have
A20 CU Ai.
Next, let x € U²₁ A₁. Then € A; for [Select]
But A, CA20 for [Select]
[Select]
Hence U2₁A = A20.
i=1,2,..., 20, so
€ A20. Thus UA C A 20.
20
i=1,2,..., 20.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9b346ae-ef24-4d99-babf-e95763a360cd%2Fbc81af7a-5fb6-42a6-adf3-f5697905269b%2Fuy7cmyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Claim: Consider a family = {A i EN} of sets such that
A1 CA2 CCA20 C..., then U20₁ Ai = A20.
i=1
Proof. Since the union of the family contains every set in the family as a subset, we have
A20 CU Ai.
Next, let x € U²₁ A₁. Then € A; for [Select]
But A, CA20 for [Select]
[Select]
Hence U2₁A = A20.
i=1,2,..., 20, so
€ A20. Thus UA C A 20.
20
i=1,2,..., 20.
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