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4. Find the union and intersection of these families, and prove your answers. (a) A = {A, ne N}, where A,, = {4n, 4n+ 1,..., 5n} for each natural number n. (b) A = {B: n = N), where B₁ = N. {n, n+1) for each natural number n. (c) A = {C₁; n = N}, where C = {1-n, n 4} for each natural - number n. (d) A = {D₂: ze Z}, where D₂ = {2z+6, 2z - 3} for all z € Z.

4. Find the union and intersection of these families, and prove your answers. (a) A = {A, ne N}, where A,, = {4n, 4n+ 1,..., 5n} for each natural number n. (b) A = {B: n = N), where B₁ = N. {n, n+1) for each natural number n. (c) A = {C₁; n = N}, where C = {1-n, n 4} for each natural - number n. (d) A = {D₂: ze Z}, where D₂ = {2z+6, 2z - 3} for all z € Z.

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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**4. Find the union and intersection of these families, and prove your answers.** **(a)** \(\mathcal{A} = \{A_n: n \in \mathbb{N}\}\), where \(A_n = \{4n, 4n + 1, \ldots, 5n\}\) for each natural number \(n\). **(b)** \(\mathcal{A} = \{B_n: n \in \mathbb{N}\}\), where \(B_n = \mathbb{N} - \{n, n + 1\}\) for each natural number \(n\). **(c)** \(\mathcal{A} = \{C_n: n \in \mathbb{N}\}\), where \(C_n = \{1 - n, n - 4\}\) for each natural number \(n\). **(d)** \(\mathcal{A} = \{D_z: z \in \mathbb{Z}\}\), where \(D_z = \{2z + 6, 2z - 3\}\) for all \(z \in \mathbb{Z}\).
Transcribed Image Text:**4. Find the union and intersection of these families, and prove your answers.** **(a)** \(\mathcal{A} = \{A_n: n \in \mathbb{N}\}\), where \(A_n = \{4n, 4n + 1, \ldots, 5n\}\) for each natural number \(n\). **(b)** \(\mathcal{A} = \{B_n: n \in \mathbb{N}\}\), where \(B_n = \mathbb{N} - \{n, n + 1\}\) for each natural number \(n\). **(c)** \(\mathcal{A} = \{C_n: n \in \mathbb{N}\}\), where \(C_n = \{1 - n, n - 4\}\) for each natural number \(n\). **(d)** \(\mathcal{A} = \{D_z: z \in \mathbb{Z}\}\), where \(D_z = \{2z + 6, 2z - 3\}\) for all \(z \in \mathbb{Z}\).
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