If `0ltalt1` and `9leble10`, then

Options

A. `9lea+ble11`
B. `9lea+blt11`
C. `9lta+ble11`
D. `9lta+blt11`

Answer

To solve the problem, we need to find the range of the sum \( a + b \) given the constraints on \( a \) and \( b \):

1. **Identify the constraints:**
- \( 0 < a < 1 \)
- \( 9 \leq b \leq 10 \)

2. **Determine the minimum value of \( a + b \):**
- The minimum value of \( a \) is just above 0 (let's denote it as \( \epsilon \), where \( \epsilon \) is a very small positive number).
- The minimum value of \( b \) is 9.
- Therefore, the minimum value of \( a + b \) is:
\[ a + b > 0 + 9 = 9 \]
- Since \( a \) cannot be exactly 0, we conclude:
\[ a + b > 9 \]

3. **Determine the maximum value of \( a + b \):**
- The maximum value of \( a \) is just below 1 (let's denote it as \( 1 - \epsilon \)).
- The maximum value of \( b \) is 10.
- Therefore, the maximum value of \( a + b \) is:
\[ a + b < (1 - \epsilon) + 10 = 11 - \epsilon \]
- Since \( a \) cannot be exactly 1, we conclude:
\[ a + b < 11 \]

4. **Combine the results:**
- From our calculations, we have:
\[ 9 < a + b < 11 \]

5. **Final conclusion:**
- The range of \( a + b \) is:
\[ (9, 11) \]

Thus, the final answer is \( 9 < a + b < 11 \).