The correct option is C 2mn−1
Let n(A)=m and n(B)=n.
We have A×B={(a,b):a∈A,b∈B}
⇒n(A×B)=n(A)×n(B)=mn
A relation from A to B is a subset of A×B.
Since A×B has mn elements, it has 2mn subsets.
Thus, there can be 2mn relations that can be defined from A to B.
⇒ The total number of non-empty relations (excluding the subset ϕ of A×B) that can be defined from A to B is 2mn−1.