Question

If n(A) = 2 and total number of possible relations from Set A to set B is 1024, then n(B) is

• A. 512
• B. 20
• C. 10
• D. 5

Answer 1

The Correct Option is D

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

The number of relations from set A to set B is given by \(2^{n(A) \cdot n(B)}\). We are given that \(n(A) = 2\) and the number of relations is 1024. So, we have:

\(2^{2 \cdot n(B)} = 1024\)

Since \(1024 = 2^{10}\), we have:

\(2^{2 \cdot n(B)} = 2^{10}\)

Therefore, \(2 \cdot n(B) = 10\), which means \(n(B) = 5\).

Answer: (D) 5

Answer 2

If $ n(A) = m $ and $ n(B) = n $, then the total number of relations from $ A $ to $ B $ is:

$$ 2^{mn}. $$

Here, $ 2^{mn} = 1024 = 2^{10} $, and $ n(A) = m = 2 $. Thus:

$$ 2n = 10 \implies n = 5. $$

Therefore, $ n(B) = 5 $.