Question

Two sets $A\&B$ such that $n\left(A\right)=p$ and $n\left(B\right)=q,$ then the number of functions from $A\to B$ is , and from $B\to A$ is

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

Answer 1

Answer: (B), (C)

$q^p$

Given two sets $A\&B$ such that
$n\left(A\right)=p\&n\left(B\right)=q$
We know that number of functions from $A\to B=n(B{)}^{n\left(A\right)}=q^p$
Similarly, the number of functions from $B\to A=p^q$