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(C) relation on a set $A$ is defined as a subset of the Cartesian product $A 	imes A$.Given $n(A) = n$,the number of elements in the Cartesian produc

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$2^{n^2}$

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(C) relation on a set $A$ is defined as a subset of the Cartesian product $A 	imes A$.Given $n(A) = n$,the number of elements in the Cartesian product $A 	imes A$ is $n(A 	imes A) = n(A) 	imes n(A) = n 	imes n = n^2$.The total number of subsets of a set with $m$ elements is $2^m$.Therefore,the total number of relations on set $A$ is the number of subsets of $A 	imes A$,which is $2^{n(A 	imes A)} = 2^{n^2}$.

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

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