Question

Let $A=\{u,v,w,z\};B=\{3,5\}$, then the number of relations from $A$ to $B$ is

• A. $256$
• B. $1024$
• C. $512$
• D. $64$

Answer 1

The correct option is A $256$

Given
$A=\{u,v,w,z\};B=\{3,5\}$
Here, number of element in set $A$ is $n\left(A\right)=4$
And number of element in set $B$ is $n\left(B\right)=2$
$\therefore$ Number of relations from $A$ to $B$
$=2^{n\left(A\right).n\left(B\right)}=2^{4\times 2}=2^8=256$