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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

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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.

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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.

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