Question

Let $A=$ {$1,2$} and $B=$ {$3,4$}. Find the number of relations from $A$ to $B$.

Answer 1

Given
$A=$ {$1,2$} and $B=$ {$3,4$}

Cartesian product of sets $A$ and $B$.
$A\times B=$ {$(1,3),(1,4),(2,3),(2,4)$}

Finding number of subsets of $A\times B$
As $n(A\times B)=4$
So, number of subsets of $A\times B$ will be $=2^{n(A\times B)}=2^4$
Hence, the number of relations from $A$ to $B$ is $2^4=16$