Is there a smart way to dertermine wether a relation is called a partial order.

For a relation to be a partial order (dont know how you describe it) it has to be reflexive, antisymmetric and transitive.

reflexive: aRb <=> aRa

tansitive aRb <=> aRb and bRc => aRc

antisymmetric: aRb <=> aRb and bRa => a=b

Can you help me out to dertermine these?

xR1y <=>x + y = or <0

xR2y <=>x − y = or <0

xR3y <=>x + y < 0