Does the following equation show transitive nature, symmetric and reflexive?

Question

Does the following equation show transitive nature, symmetric and reflexive? $$d(a,b) = \lvert a-b \rvert \le 2 $$

I am really having trouble with this problem any help would be appreciated. I have tried to rearrange it but am not sure how to do it with the absolute value problem.

Answer 1

Hint:

This relation is reflexive if $d(a,a) \leq 2$ for all $a$. Which is true as $d(a,a) = 0$.

Symmetric: does $d(a,b) \leq 2$ imply $d(b,a) \leq 2$ for all $a, b$?

Transitive: does $d(a,b) \leq 2$ and $d(b,c) \leq 2$ imply $d(a,c) \leq 2$ for all $a,b,c$?