Question

If $ n(A) = 7 $ and the number of relations from A to B is 128. Then find } $ n(B) $.

• A. \( 7 \)
• B. \( 8 \)
• C. \( 16 \)
• D. \( 14 \)

Hint:

The number of relations from set \( A \) to set \( B \) is simply the product of the sizes of the sets.

Answer 1

The Correct Option is C

The number of relations from a set \( A \) to a set \( B \) is given by: \[ n(A) \times n(B) \] We are given that \( n(A) = 7 \) and the number of relations is 128. Therefore, we have: \[ 7 \times n(B) = 128 \] Solving for \( n(B) \): \[ n(B) = \frac{128}{7} = 16 \]
Thus, \( n(B) = 16 \). Hence, the correct answer is \( 16 \).