Answer to Question #148118 in Discrete Mathematics for Promise Omiponle

Question #148118
Let R be an equivalence relation on Z, which has P={{±i}|i ∈ N} as its collection of equivalence classes. Describe the equivalence relation R.
1
Expert's answer
2020-12-15T07:20:00-0500

By definition, "(a,b)\\in R" if and only if "a,b\\in A" for some "A\\in P."


Let us describe the equivalence relation "R". It follows that for "i\\in\\mathbb N" we have that "a,b\\in\\{\\pm i\\}" if and only if "|a|=|b|=i" . Therefore, "a,b\\in\\{\\pm i\\}" for some "i\\in\\mathbb N" if and only if "|a|=|b|" .

               We conclude that "(a,b)\\in R" if and only if "|a|=|b|".

 


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