We define the relation R on the set $A=\{ -8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8 \}.$
so that $xRy$ if and only if $x+4y$ is dividable with $5$.
Ok so how should i define this $R$ with $x$ and $y$?
Should I try with every element = $x$ and with every element = $y$? Is not that very many combinations to consider?
HINT: $5|(x+4y)$ if and only if $x \equiv y \mod 5$. Then can you find the (equivalence) classes (if you did not learn about it, you can try to find the elements which are equivalent modulo $5$)?
As an example, $\{-5,0,5\}$ is one of the classes because $-5 \equiv 0 \equiv 5 \mod 5$. There are four more such classes and when you find them, you are basically done because you know that $x \equiv y \mod 5$ so $x$ and $y$ should be chosen from the same class.