Question

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:

• A. 9
• B. $9^2$
• C. $2^9$
• D. $2^3$

Hint:

Relations are subsets of $A \times B$, so the formula is $2^{\text{Product of counts}}$.

Answer 1

The Correct Option is C

Step 1: Concept
The number of relations from set A to set B is $2^{n(A) \times n(B)}$.

Step 2: Meaning
$A = \{2, 4, 6\}$ so $n(A) = 3$. $B = \{2, 3, 5\}$ so $n(B) = 3$.

Step 3: Analysis
The total number of elements in the Cartesian product $A \times B$ is $3 \times 3 = 9$.

Step 4: Conclusion
The number of relations is $2^9$. Final Answer: (C)