Suppose you take the relation R containing just the ordered pair <1,0>. Can this be a relation on the empty set?
One line of reasoning might be that R is an equivalence relation on the empty set, because there is nothing in the empty set that could make R irreflexive, etc.
But on the other hand, how can R be a subset of the Cartesian product of the empty set, given that R itself is not empty but contains the ordered pair <1,0>?
I feel I'm confused somewhere and would appreciate your help!