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Define a relation ~ on the set N of natural numbers bya ~ b iff a = b . 10k for some k E

Chapter 9, Problem 9.8

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QUESTION:

Define a relation ~ on the set N of natural numbers bya ~ b iff a = b . 10k for some k E Z.(a) Prove that ~ is an equivalence relation on N. State clearly the properties of Z that are usedin the proof.(b) Give a complete set of equivalence class representatives.

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QUESTION:

Define a relation ~ on the set N of natural numbers bya ~ b iff a = b . 10k for some k E Z.(a) Prove that ~ is an equivalence relation on N. State clearly the properties of Z that are usedin the proof.(b) Give a complete set of equivalence class representatives.

ANSWER:

Step 1 of 4

Let us first prove  is reflexive. Let  We see that here. Which is an integer. Therefore. Hence  is reflexive.

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