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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(choose chapter or problem)
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.
Questions & Answers
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.