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Define a relation ~ on JR bya ~ b iff lal = Ibl.(a) Prove that ~ is an equivalence
Chapter 9, Problem 9.7(choose chapter or problem)
Define a relation ~ on JR bya ~ b iff lal = Ibl.(a) Prove that ~ is an equivalence relation on JR. State clearly the properties of the relation =on JR that are used in the proof.(b) Give a complete set of equivalence class representatives.
Questions & Answers
QUESTION:
Define a relation ~ on JR bya ~ b iff lal = Ibl.(a) Prove that ~ is an equivalence relation on JR. State clearly the properties of the relation =on JR that are used in the proof.(b) Give a complete set of equivalence class representatives.
ANSWER:Step 1 of 3
Consider the on defined by if and only if .
(a)
As per the reflexive property of on , it is known that for all which gives for all .
Therefore, for all and therefore, is reflexive.
If then . As per the symmetric property of on , gives which also gives and therefore, is symmetric.