Question

If $A,B$ two sets such that $n\left(A\right)=p,n\left(B\right)=q$. Then number of functions from set $A$ to set $B$ are

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

Answer 1

The correct option is B $q^p$

Let $A,B$ two sets such that $n\left(A\right)=p,n\left(B\right)=q$
A function from $A$ to $B$ is a relation in which every element of set $A$ have a unique image in set $B$.
Since every element of Set $A$ have exactly ${}^{\prime }{q}^{\prime }$ choices to associate with any one element of set $B$.
Then number of functions from set $A$ to set $B$ are
$q\cdot q\cdot q\cdot \cdots \cdot q\left(p\text{times}\right)=q^p$