Solution for problem 9.15 Chapter 9
For x, Y E lR, let X ~ Y mean that X - Y is an integer. Verify that "'- is an
Modern Algebra: An Introduction | 6th Edition
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.
Step 1 of 3
For , let mean that
Since for all we have that for all and therefore is reflexive.