If `A={1,2,3)` and `B={a,b}`, then the number of functions from A to B is

Options

A. 3
B. 6
C. 8
D. 12

Answer

To find the number of functions from set A to set B, we can follow these steps:

### Step 1: Identify the sets
We have two sets:
- Set A = {1, 2, 3}
- Set B = {a, b}

### Step 2: Determine the number of elements in each set
- The number of elements in set A (denoted as m) is 3 (since A has three elements: 1, 2, and 3).
- The number of elements in set B (denoted as n) is 2 (since B has two elements: a and b).

### Step 3: Use the formula for the number of functions
The formula for the number of functions from set A to set B is given by:
\[ \text{Number of functions} = n^m \]
where n is the number of elements in set B and m is the number of elements in set A.

### Step 4: Substitute the values into the formula
Here, we have:
- n = 2 (number of elements in set B)
- m = 3 (number of elements in set A)

Substituting these values into the formula:
\[ \text{Number of functions} = 2^3 \]

### Step 5: Calculate the result
Now, we calculate \( 2^3 \):
\[ 2^3 = 8 \]

### Conclusion
The total number of functions from set A to set B is 8.

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