Step 1 The definition of the reflexive property is: For every . We see that , and for every variable it relates to itself given that the relation . Definition of antisymmetric is: whenever are such that aRb and bRa , then necessarily . With , we see with our given R we see that this is antisymmetric. Step 2 With the definition of symmetric: , we see that this is symmetric. So this relation is reflexive, antisymmetric and symmetric.