Question

If $R$ is a relation on a finite set having $n$ elements, then the number of relations on $A$ is

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

Answer 1

Answer: (B)

Number of relations from $A$ to $B$, if $A$ has $m$ elements and $B$ has $n$ elements $=2^{m\times n}$
$\therefore$ Required relation on $A=2^{n\times n}=2^{n^2}$