Give an example of a set A = {1, 2, ..., k} for a smallest k = N containing subsets A₁, A2, A3 such that |A¡ — A ¡| = |A; − A¡| = |i − j| for every two integers i and j with 1 ≤ i ≤ j≤ 3.
Give an example of a set A = {1, 2, ..., k} for a smallest k = N containing subsets A₁, A2, A3 such that |A¡ — A ¡| = |A; − A¡| = |i − j| for every two integers i and j with 1 ≤ i ≤ j≤ 3.
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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I understand sets and cardinalities, the following question just really confuses me, I dont know where to begin, so if able please explain the following question in detail step by step, how do i approach these kind of questions? Thank you in advance.
![Give an example of a set A = {1, 2, . . ., k} for a smallest k ← N containing subsets
A₁, A2, A3 such that |A; — Aj| = |Aj − A¡| = |i − j| for every two integers i and j
with 1 ≤i<j≤ 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e237d3f-b8e6-4775-a6f9-5671b153aef2%2Fc0831bde-ff39-4ba0-8486-368e77432b36%2Fo0l6aam_processed.png&w=3840&q=75)
Transcribed Image Text:Give an example of a set A = {1, 2, . . ., k} for a smallest k ← N containing subsets
A₁, A2, A3 such that |A; — Aj| = |Aj − A¡| = |i − j| for every two integers i and j
with 1 ≤i<j≤ 3.
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