Question

Given two sets $A\&B$ such that $n\left(A\right)=p,n\left(B\right)=q.$ Then the number of relations from $A\text{to}B$ is

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

Answer 1

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

Given two sets $A,B$ such that $n\left(A\right)=p,n\left(B\right)=q$ such that
$n\left(A\right)=p\&n\left(B\right)=q$
Now, the number of ordered pairs in $A\times B=n(A\times B)=pq$

Any relation from $A\text{to}B$ will be the subset of $(A\times B).$
Now, number of subsets of $A\times B=2^{pq}$
Hence, there are $2^{pq}$ relations from $BtoA.$