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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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 ~,
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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