Question

If $R$ is relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is

• A. $2^{mn}$
• B. $2^{mn}-1$
• C. $2mn$
• D. $m^n$

Answer 1

The correct option is A $2^{mn}$

$A\times B$ will have $mn$ ordered pairs. Each subset of
$A\times B$ will be a relation. The number of subsets of a
set consisting of $mn$ elements will be $2^{mn}$.