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(C) Given that $n(A) = 2$ and $n(B) = 3$.The number of elements in the Cartesian product $A 	imes B$ is $n(A 	imes B) = n(A) 	imes n(B) = 2 	imes

Vedclass · Accepted Answer

$64$

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(C) Given that $n(A) = 2$ and $n(B) = 3$.The number of elements in the Cartesian product $A 	imes B$ is $n(A 	imes B) = n(A) 	imes n(B) = 2 	imes 3 = 6$.$A$ relation from set $A$ to set $B$ is defined as any subset of the Cartesian product $A 	imes B$.The total number of relations from $A$ to $B$ is equal to the total number of subsets of $A 	imes B$.The number of subsets of a set with $m$ elements is $2^m$.Therefore,the total number of relations is $2^{n(A 	imes B)} = 2^6 = 64$.Thus,the correct option is $(c)$.

Two finite sets $A$ and $B$ are such that $n(A) = 2$ and $n(B) = 3$. Then the total number of relations from $A$ to $B$ is:

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