Let the relation - on the natural numbers N be defined as follows: if n is even, then n ~ n + 1; if n is odd, then n ~ n - 1. Furthermore, for every n, let n - n. (a) Prove that - is an equivalence relation on N. (b) What is the equivalence class of 5? (c) Describe the set {[n] | n E N} of all equivalence classes of ~,
Let the relation - on the natural numbers N be defined as follows: if n is even, then n ~ n + 1; if n is odd, then n ~ n - 1. Furthermore, for every n, let n - n. (a) Prove that - is an equivalence relation on N. (b) What is the equivalence class of 5? (c) Describe the set {[n] | n E N} of all equivalence classes of ~,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![Let the relation - on the natural numbers N be defined as follows: if n is even, then
n ~ n + 1; if n is odd, then n ~ n - 1. Furthermore, for every n, let n - n.
(a) Prove that ~ is an equivalence relation on N.
(b) What is the equivalence class of 5?
(c) Describe the set {[n] | n E N} of all equivalence classes of ~,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5655175-49d2-4db6-a7fd-785d70a02cda%2F4688fac4-03f3-4da9-b245-3ecb6a2c89dc%2F77c9i4m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let the relation - on the natural numbers N be defined as follows: if n is even, then
n ~ n + 1; if n is odd, then n ~ n - 1. Furthermore, for every n, let n - n.
(a) Prove that ~ is an equivalence relation on N.
(b) What is the equivalence class of 5?
(c) Describe the set {[n] | n E N} of all equivalence classes of ~,
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