Question

Two sets A and B have p and q elements respectively. Then the number of relations from B to A is

• A. $p+q$
• B. $pq$
• C. $q^p$
• D. $2^{pq}$

Answer 1

The correct option is D $2^{pq}$

$n\left(A\right)=pn\left(B\right)=qn(B\times A)=pq$
Any relation from B to A is a subset of $(B\times A).$ Number of subsets of $B\times A=2^{pq}$
Hence, there are $2^{pq}$ relations from B to A.