On the real axis ,If A=[0,3] and B= [2,6] ,than find the following
(iv) `A-B`

Answer

To find \( A - B \) where \( A = [0, 3] \) and \( B = [2, 6] \), we need to determine the elements that are in set \( A \) but not in set \( B \).

### Step-by-Step Solution:

1. **Identify the Sets**:
- Set \( A = [0, 3] \) includes all real numbers from 0 to 3, including the endpoints 0 and 3.
- Set \( B = [2, 6] \) includes all real numbers from 2 to 6, including the endpoints 2 and 6.

2. **Visualize the Sets on the Number Line**:
- On a number line, set \( A \) is represented as a line segment from 0 to 3.
- Set \( B \) is represented as a line segment from 2 to 6.
- The overlap between sets \( A \) and \( B \) occurs from 2 to 3.

3. **Determine the Elements in \( A \) but not in \( B \)**:
- The elements of set \( A \) are from 0 to 3.
- The elements of set \( B \) that overlap with \( A \) are from 2 to 3.
- Therefore, when we subtract set \( B \) from set \( A \), we need to remove the overlapping part, which is from 2 to 3.

4. **Calculate \( A - B \)**:
- From set \( A \), we have:
- The part from 0 to 2 remains (which is \( [0, 2) \)).
- The part from 2 to 3 is removed because it overlaps with set \( B \).
- Thus, the result of \( A - B \) is:
\[ A - B = [0, 2) \]
- Here, 0 is included (closed bracket) and 2 is not included (open bracket).

### Final Answer:
\[ A - B = [0, 2) \]