Question

If $ n(A) = 4 $ and $ n(B) = 2 $, then the number of surjections from A to B is:

• A. 14
• B. 2
• C. 8
• D. None of these

Hint:

The formula for the number of surjections depends on the sizes of both the sets, and the number of surjections increases with the size of the set.

Answer 1

The Correct Option is C

Step 1: Understanding Surjections
A surjection (or onto function) from a set \( A \) to a set \( B \) is a function where every element of \( B \) has at least one element from \( A \) mapping to it.
The number of surjections from a set \( A \) to a set \( B \) is given by the formula: \[ \text{Number of surjections} = B^A - \text{(non-surjective functions)} \] For a set \( A \) with 4 elements and a set \( B \) with 2 elements, the total number of surjections can be computed using the formula for surjections.
Step 2: Applying the Formula
From the formula, we can calculate the number of surjections as \( 8 \).

Step 3: Conclusion
Thus, the number of surjections from \( A \) to \( B \) is 8.