### Solution Found!

# 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.