An interesting question, and one I must admit I am not too sure about. I have certainly never seen a binary relation defined in such a way. However, I can see no reason as to why this is not valid. Essentially it says that if we take the set of ALL ordered pairs then some of them are in the subset, and others are not. That is to say, the sets are disjoint. I am pretty sure that that is all the definition is saying, and clearly it is true. (Note that I am using "clearly" in an entirely un-rigorous sense, but I can't think of any relation where this would fail).
For instance, take the binary relation on . Clearly either or as or .
Also, the bit that you made blue is merely the author (or whoever gave you the definition) making life easier for themselves. It is not really part of the definition.