Question

If number of elements in sets $A$ and $B$ are m and $n$ respectively, then the number of relations from $A$ to $B$ is

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

Answer 1

Answer: (B)

$n\left(A\times B\right)=n\left(A\right)\times n\left(B\right)=mn$
$\therefore n\left[P\left(A\times B\right)\right]=2^{mn}$
Since each relation from $A$ to $B$ is an element of $P\left(A\times B\right)$, the number of relations from $A$ to $B$ is $2^{mn}$.