Question

Let $n(A)=m$, and $n(B)=n$. Then the total number of non-empty relations that can be defined from $A$ to Bis

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

Answer 1

Answer: (D)

Given, $n(A)=m$ and $n(B)=n$
$\therefore$ Total number of relations from $A$ to $B=2^{mn}$
$\therefore$ Total number of non-empty relations from
$A$ to $B=2^{mn}-1$