Binary relations - how to find an inverse binary relation - textbook task

Question

The task is as follows: Let R be a binary relation on the set X={1,2,3,4,5,6,7,8,9}. R = { ( x,y ) | x,y ∈ X, 3 divides x − 2y }. Find the inverse relation S. Is there a different way to define the set S than just writing S={(2, 1), (5, 1), (8, 1), ...} If someone could give me a hint in the right direction it would be much appreciated.

Answer 1

You could write: $$S=\{(x,y)\in X^2\mid 3\text{ divides } y-2x\}$$where the roles of $x$ and $y$ are switched.