Statement -2 : The number of functions from A = {1, 2, 3} to B = {2008, 2009} is 8.
and
Statement-2 : The number of all possible functions from A = {1, 2, 3} to B = {2008, 2009} is 9.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement -1 is True, Statement -2 is False
D. Statement -1 is False, Statement -2 is True

Answer

To determine the validity of the statements regarding the number of functions from set A to set B, we will analyze each statement step by step.

### Given:
- Set A = {1, 2, 3} (which has 3 elements)
- Set B = {2008, 2009} (which has 2 elements)

### Step 1: Calculate the number of functions from A to B
The formula to calculate the number of functions from a set with \( m \) elements to a set with \( n \) elements is given by:
\[ n^m \]
where \( n \) is the number of elements in the codomain (set B) and \( m \) is the number of elements in the domain (set A).

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

Substituting these values into the formula gives:
\[ 2^3 = 8 \]

### Conclusion for Statement 1
The number of functions from set A to set B is indeed 8. Therefore, **Statement 1 is correct**.

### Step 3: Analyze Statement 2
Statement 2 claims that the number of all possible functions from A to B is 9.

### Step 4: Evaluate Statement 2
From our calculation in Step 2, we found that the total number of functions is 8, not 9. Therefore, **Statement 2 is false**.

### Final Conclusion
- Statement 1 is correct: The number of functions from A to B is 8.
- Statement 2 is incorrect: The number of all possible functions from A to B is not 9, it is 8.

Thus, the correct option based on the analysis is that Statement 1 is true and Statement 2 is false.

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