Question

Let A and B be finite sets containing m and n elements respectively. The number of relations that can be defined from A and B is:

• A. mn
• B. $2^{mn}$
• C. $2^{m+n}$
• D. $n^m$

Answer 1

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

Here, $O\left(A\right)=m$ and $O\left(B\right)=n$.

Hence $O(A\times B)=mn$

Since every subset of $A\times B$ is a relation from $A$ to $B$, therefore, number of relations from A to B is equal to the number of the subsets of $A\times B$, i.e., $2^{mn}$