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# hw14 - Z given by a,b | n divides a-b a Prove that â‰ n is...

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Intro to Abstract Math Homework 14 Fall 2009 Due October 9 Exercise 40. Recall the equivalence relation Q = { (( a, b ) , ( c, d )) | ad - bc = 0 } on Z × N . a. Determine the equivalence class of ( a, b ) Z × N . b. Write out several elements (at least 5) of [(1 , 2)]. Do the same for [(3 , 4)]. Do you see a pattern? Exercise 41. Let n N , n 2. Let n denote the relation on
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Unformatted text preview: Z given by { ( a,b ) | n divides a-b } . a. Prove that â‰¡ n is an equivalence relation on Z . b. Determine the equivalence class of a âˆˆ Z . c. By looking at a few cases with small values of n , make a guess as to how many equiva-lence classes there are....
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