Question

If $R$ is a 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 $2^{mn}$

$R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements.
Number of elements in $A\times B$ $=mn$
No of relations $=$ number of subsets of $A\times B$ $=2^{mn}$
Hence, option A is correct.