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 $B$ are
Step-by-Step Solution
Key Concept: The number of relations from set $A$ to set $B$ is $2^{|A| \times |B|}$ since each relation is a subset of the Cartesian product.
Given $A = \{2, 4, 6\}$ and $B = \{2, 3, 5\}$, the Cartesian product $A \times B$ contains $3 \times 3 = 9$ elements. The total number of relations from $A$ to $B$ equals the number of subsets of $A \times B$, which is $2^9 = 512$.
Correct Answer: 512