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For x, Y E lR, let X ~ Y mean that X - Y is an integer. Verify that "'- is an
Chapter 9, Problem 9.15(choose chapter or problem)
QUESTION:
For x, Y E lR, let X ~ Y mean that X - Y is an integer. Verify that "'- is an equivalence relation.Describe the equivalence classes geometrically, with the elements of JR identified with thepoints on a line in the usual way. Give a complete set of equivalence class representatives.
Questions & Answers
QUESTION:
For x, Y E lR, let X ~ Y mean that X - Y is an integer. Verify that "'- is an equivalence relation.Describe the equivalence classes geometrically, with the elements of JR identified with thepoints on a line in the usual way. Give a complete set of equivalence class representatives.
ANSWER:Step 1 of 3
For , let mean that
Since for all we have that for all and therefore is reflexive.