Check if a relation is reflexive, symmetric and transitive
&quot;If xRy and yRz&quot;: Look at the definition of R. You have x = 0 and y ≥ 0 because xRy. You have y = 0 and z ≥ 0 because of yRz. If you have xRy and yRz then you have x = 0 and z ≥ 0, therefore xRz. So R is transitive.
In total you know that x = 0, y = 0 and z ≥ 0, so you also have yRx, although nobody cares much about that.