Sets A = even natural numbers < 8 and B = prime numbers < 7. Find the number of relations from A to B.

Set $A$ is the set of even natural numbers less than 8.
The natural numbers are $\{1, 2, 3, \dots\}$.
The even natural numbers less than 8 are $\{2, 4, 6\}$.
So, $A = \{2, 4, 6\}$.
The number of elements in set $A$ is $n(A) = 3$.

Set $B$ is the set of prime numbers less than 7.
The prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
The prime numbers less than 7 are $\{2, 3, 5\}$.
So, $B = \{2, 3, 5\}$.
The number of elements in set $B$ is $n(B) = 3$.

The number of elements in $A \times B$ is given by the product of the number of elements in $A$ and the number of elements in $B$.

A relation from set $A$ to set $B$ is any subset of $A \times B$.
If a set has $m$ elements, then the number of its subsets is $2^m$.
Since $A \times B$ has 9 elements, the total number of possible relations from $A$ to $B$ is $2^{n(A \times B)}$.

The calculated number of relations is $2^9$, which corresponds to option (A).