Does the relation aRb if (a+b) is not divisible by 4 has transitive property? I recently encounter an programming problem in which I was to make subsets of set 'S' as following -
{ a + b should not be divisibe by 'k' where 'a' and 'b' are elements of S }

Of course I could just brute force through it and get an answer but I got interested in the fact that is this property transitive i.e. if a+b is not divisible by 'k' and if a+c is not divisible by 'k' then b+c is also not divisible by 'k'.
I could neither prove it not find an counter-example. 

Extra question - this relation is definately not reflective, but would these subsets still make equivalance classes? why or why not?

Edit - thank you for your answers. Even though it seems like  a rather dumb question in hindsight, I appreciate your answers.
Lack of reflexiveness already makes it not an equivalence relation, so they can't be equivalence classes. But note also that $1+2$ is not divisible by $4$, $2+3$ is not divisible by $4$, but $1+3$ is divisible by $4$, so transitivity fails as well.
Counter-example :-

Let k = 4, a = 8, b = 6 and c = 10