Lets say we have a subset of $\mathbb{Z}$ that is $$A = \{-2,-1,0,1\}$$
And we have a relation $R$ that is defined on the set $A$ such that $$xRy = \{(x,y) \in AxA: y < 0\}$$
Is this the complete set of $R$ or is it wrong?: $$R = \{(-2,-2),(-1,-2),(0,-2),(1,-2),(-2,-1),(-1,-1),(0,-1),(1,-2)\}$$
Your answer is correct. In fact, you have to save all tge tuples $(x,y)$ such that $y<0$ and $x$ can be all number in the set $A$. So, we have: $$R = \{(-2,-2),(-1,-2),(0,-2),(1,-2),(-2,-1),(-1,-1),(0,-1),(1,-2)\} $$