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(A) Step $1$: Identify the elements of set $A$. The even natural numbers less than $8$ are $2, 4, 6$. So,$A = \{2, 4, 6\}$.Step $2$: Identify the elem

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$2^9$

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(A) Step $1$: Identify the elements of set $A$. The even natural numbers less than $8$ are $2, 4, 6$. So,$A = \{2, 4, 6\}$.Step $2$: Identify the elements of set $B$. The prime numbers less than $7$ are $2, 3, 5$. So,$B = \{2, 3, 5\}$.Step $3$: Calculate the number of elements in the Cartesian product $A 	imes B$. The number of elements $n(A) = 3$ and $n(B) = 3$. Thus,$n(A 	imes B) = n(A) 	imes n(B) = 3 	imes 3 = 9$.Step $4$: The number of relations from $A$ to $B$ is the number of subsets of $A 	imes B$,which is given by $2^{n(A 	imes B)} = 2^9$.

If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$,then the number of relations from $A$ to $B$ is

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