Question

Let \( A = \{ 1, 2, 3, \dots, n \} \) and \( B = \{ a, b, c, \dots \} \), then the number of functions from A to B that are onto is

• A. \( 3^{n - 2} \)
• B. \( 3^{n - 1} \)
• C. \( 3^{n - 2} - 1 \)
• D. \( 3^{n - 2} \)

Hint:

The number of onto functions from a set \( A \) to a set \( B \) is given by the formula involving powers of the number of elements in \( B \).

Answer 1

The Correct Option is D

Step 1: Using the onto function formula.
The number of onto functions from a set \( A \) to a set \( B \) can be calculated using the formula for the number of onto functions, which is \( 3^{n - 2} \).

Step 2: Conclusion.
Thus, the correct answer is option (D).

Final Answer: \[ \boxed{\text{(D) } 3^{n - 2}} \]