Question

If \( A = \{1, 2, 3\}, B = \{a, b\} \), then the number of functions from A to B will be:

• A. 6
• B. 8
• C. 9
• D. 5

Hint:

To find the number of functions from set \( A \) to set \( B \), use the formula \( |B|^{|A|} \), where \( |A| \) and \( |B| \) are the number of elements in sets \( A \) and \( B \), respectively.

Answer 1

The Correct Option is B

Step 1: Determine the number of elements in sets \( A \) and \( B \). 
The set \( A \) has 3 elements, and set \( B \) has 2 elements. The number of functions from set \( A \) to set \( B \) is given by the formula \( |B|^{|A|} \), where \( |A| \) and \( |B| \) represent the number of elements in sets \( A \) and \( B \), respectively. 

Step 2: Apply the formula. 
Substituting the values \( |A| = 3 \) and \( |B| = 2 \), we get: \[ 2^3 = 8 \] 

Step 3: Conclusion. 
Thus, the total number of functions is \( 8 \), which is the correct answer.