Question

If n(A) = m and n(B) = n, then find the total number of relations that exist between A and B.

• A. ${\left(mn\right)}^2$
• B. $2^{mn}$
• C. $2^m$
• D. $2^n$

Answer 1

The correct option is B $2^{mn}$

The total number of relations that can be formed between two sets is the number of subsets of their Cartesian product.
Here, n(A) = m and n(B) =n
$\Rightarrow$ n(AXB)= mn
Hence, Number of relations between A and B = $2^{mn}$
NOTE: If n(A) = m, then the number of subsets of set A = $2^m$