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Question

(A) relation $R$ from set $A$ to set $B$ is defined as a subset of the Cartesian product $A 	imes B$.Given that set $A$ has $m$ elements and set $B$

Vedclass · Accepted Answer

$2^{mn}$

Vedclass · Answer

(A) relation $R$ from set $A$ to set $B$ is defined as a subset of the Cartesian product $A 	imes B$.Given that set $A$ has $m$ elements and set $B$ has $n$ elements,the number of elements in the Cartesian product $A 	imes B$ is $|A 	imes B| = |A| 	imes |B| = m 	imes n = mn$.The total number of subsets of a set with $k$ elements is $2^k$.Since a relation is any subset of $A 	imes B$,the total number of relations from $A$ to $B$ is the number of subsets of $A 	imes B$.Therefore,the number of relations is $2^{mn}$.

If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements,then the number of relations from $A$ to $B$ is:

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