Question

If $n(A) = 2$ and the number of relations from set A to set B is 1024, then $n(B)$ is

• A. 2
• B. 5
• C. $2^5$
• D. $5^2$

Hint:

It is very beneficial to memorize the powers of 2 up to $2^{10} = 1024$ for competitive exams. It speeds up problems involving subsets, combinations, and binary calculations significantly.

Answer 1

The Correct Option is B

Step 1: Given Data
\[ n(A) = 2, \text{Number of relations} = 1024 \]
Step 2: Use Formula
Number of relations from $A$ to $B$: \[ = 2^{n(A)\cdot n(B)} \] Let $n(B) = m$: \[ 2^{2m} = 1024 \]
Step 3: Convert to Same Base
\[ 1024 = 2^{10} \] \[ 2^{2m} = 2^{10} \]
Step 4: Equate Powers
\[ 2m = 10 \Rightarrow m = 5 \]
Step 5: Final Answer
\[ \boxed{n(B) = 5} \]