A subset S of Zis said to be shifty if for every s ∈S, we have either s + 1 ∈S or s −1 ∈S. a. Let S denote the set S = {n ∈Z: n is not a multiple of 5 and n is not a multiple of 11}. Is S shifty? Explain. b. Prove or disprove: The union of two shifty sets is shifty. c. Prove or disprove: Every non-empty shifty set contains an even integer.

A subset S of Zis said to be shifty if for every s ∈S, we have either s + 1 ∈S or s −1 ∈S. a. Let S denote the set S = {n ∈Z: n is not a multiple of 5 and n is not a multiple of 11}. Is S shifty? Explain. b. Prove or disprove: The union of two shifty sets is shifty. c. Prove or disprove: Every non-empty shifty set contains an even integer.

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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