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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Question

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.

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