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Give a complete set of equivalence class representatives for the equivalence relation in

Chapter 9, Problem 9.10

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QUESTION:

Give a complete set of equivalence class representatives for the equivalence relation in Example9.2.

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QUESTION:

Give a complete set of equivalence class representatives for the equivalence relation in Example9.2.

ANSWER:

Step 1 of 2

Let  be the set of all lines in a plane which has rectangular coordinate system.

For ,

Consider  which means that both the lines  have equal and undefined slopes which is an equivalence relation on .

The set of lines which are equivalent to a line  consists of  and all lines in  that are parallel to .

 

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