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

Question

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 ??

Answer 1

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