Question

If $n\left(A\right)=2,n\left(B\right)=m$ and the number of relation from $A$ to $B$ is $64$, then the value of $m$ is

• A. $6$
• B. $3$
• C. $16$
• D. $8$

Answer 1

The correct option is B $3$

The number of relations between sets can be calculated using $2^{mn}$ where m and n represent

the number of members in each set.

Given that $n\left(A\right)=2$ and $n\left(B\right)=m$

So,

$2^{2m}=64$

$2^{2m}=2^6$

On comparing powers of 2 we get,

$2m=6$

$m=3$