Question

If set $A$ has $4$ elements, set $B$ has $2$ elements and $A,B$ have one element in common, then the number of non trivial relations from $A$ to $B$ is

Answer 1

$n\left(A\right)=4,n\left(B\right)=2$
Number of relations from $A$ to $B=2^{n\left(A\right)n\left(B\right)}=2^8$
$\therefore$ Number of non trivial relations from $A$ to $B=2^8-2=256-2=254$
($\because$ Void and universal relation are called trivial relations)