# Is the relation $\{ (a,b) \in\Bbb Z^2 : |a-b| \le 10 \}$ an equivalence relation or not ??

Is the relation ↖ an equivalence relation or not ??

I know we are supposed to prove that it is reflexive , transitive and symmetric . I found that it is an equivalence relation but i am not sure , so can you please take a look and tell me if it is correct or not ??

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Are you sure that it’s transitive? What if $a=0,b=10$, and $c=20$? –  Brian M. Scott Nov 30 '12 at 12:45
Yes , you are right . It is not transitive in this case . Thank you so much. I appreciate your help. –  user51287 Nov 30 '12 at 12:49
You’re welcome. –  Brian M. Scott Nov 30 '12 at 13:02
@BrianM.Scott It seems your question/comment was "spot on." Perhaps you'd like to post an answer to the question? –  amWhy Nov 30 '12 at 15:34
@amWhy: Done! $~$ –  Brian M. Scott Nov 30 '12 at 19:59

HINT: Are you sure that it’s transitive? What if $a=0,b=10$, and $c=20$?