The standard definition of a relation of an arbitrary set A is a subset of the set product of A, AxA. Is it okay to define relation R to be a subset of the set product AxA such that R has at least one property P (i.e. inequality, equality, difference, etc.), where any two element of a relation obeys P, and any two element of a set A either obeys P or not? The standard definition of a relation seems to me little ambiguous.