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## 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

Problem 9.15

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.

**Accepted Solution**

Step-by-Step Solution:

Step 1 of 3

For , let mean that

Since for all we have that for all and therefore is reflexive.

###### Chapter 9, Problem 9.15 is Solved

**Step 2 of 3**

**Step 3 of 3**

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For x, Y E lR, let X ~ Y mean that X - Y is an integer. Verify that "'- is an