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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
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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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.
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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