I have some doubts regarding relations and binary relations in particular.This is what I understand :
1) The graph $G_R$ of a relation R on X and Y is the subset of X × Y defined by $G_R$ = {(x, y) ∈ X × Y : xRy} . This graph contains all of the information about which elements are related. Conversely, any subset G ⊂ X×Y defines a relation R by: xRy if and only if (x, y) ∈ G. Thus, a relation on X and Y may be (and often is) defined as subset of X × Y . Is it true that for sets, it doesn’t matter how a relation is defined, only what elements are related ?
2)Since any subset of A × B is a relation from A to B, it follows that the number of relations from A to B is $2^{|A×B|} = 2^{|A|·|B|}$.So, if A & B are null sets $\implies$ no. of relations is 1. So, will it lead to the statement that there exist at least one relationship between any two sets in the universe?