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Solutions for Modern Algebra: An Introduction | 6th Edition | ISBN: 9780470384435 | Authors: John R. Durbin 9780470384435

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