Question

If the number of elements of the sets $A$ and $B$ is $p$ and $q$, respectively. Then, the number of relations from the set $A$ to the set $B$ is

• A. $2^{\left(p+q\right)}$
• B. $2^{\left(pq\right)}$
• C. $p+q$
• D. $pq$

Answer 1

The correct option is B

$2^{\left(pq\right)}$

The explanation for the correct answer

Given: Set $A$and $B$

Number of elements in $A$is $p$

Number of elements in $B$is $q$

The number of relations from a set to another set is given by $2^{mn}$where $m$and $n$are the number of elements.

Number of elements from $A$to $B$ is $2^{pq}$

Hence option (B) is the correct answer.