If n(A) = 5 and (n)B = 7, then the number of relations on A $$\times$$ B is

To calculate the number of relations from set $$A$$ to set $$B$$, we first find the number of elements in their Cartesian product, $$n(A \times B)$$, which is $$n(A) \times n(B) = 5 \times 7 = 35$$. Since a relation is defined as any subset of the Cartesian product $$A \times B$$, and a set with $$m$$ elements has $$2^m$$ possible subsets, the total number of relations is $$2^{35}$$. This formula accounts for every possible combination of ordered pairs that can be formed between the two sets.