Question

If $:n\left(A\right)=m,$ then number of relations in $A$ are

• A. $2^m$
• B. $2^m-2$
• C. $2^{m^2}$
• D. None of these

Answer 1

The correct option is C $2^{m^2}$

Given $:n\left(A\right)=m$ Relation in a set $A$ is subset of
$A\times A$ For Number of subset of $A$ We have
$n(A\times A)=n\left(A\right)\times n\left(A\right)=m^2$
$\therefore$ Number of subset of $A\times A=2^{m^2}$
every subset of $A\times A$ is a relation
$\therefore$ Number of relations in A is $2^{m^2}=2^{m\times m}$