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.