Let n(A) = n. Then the number of all relation | vedclass

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(C) The set $A$ has $n$ elements,so $n(A) = n$. The Cartesian product $A 	imes A$ contains $n 	imes n = n^2$ elements. $A$ relation on set $A$ is de

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$2^{n^2}$

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(C) The set $A$ has $n$ elements,so $n(A) = n$. The Cartesian product $A 	imes A$ contains $n 	imes n = n^2$ elements. $A$ relation on set $A$ is defined as any subset of $A 	imes A$. The total number of subsets of a set with $m$ elements is $2^m$. Since $A 	imes A$ has $n^2$ elements,the total number of subsets of $A 	imes A$ is $2^{n^2}$. Therefore,the number of all relations on $A$ is $2^{n^2}$. Thus,the correct option is $C$.

Let $n(A) = n$. Then the number of all relations on $A$ is

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