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

Answer

To find the intersection of the sets A and B, we will follow these steps:

### Step 1: Identify the sets
We have two sets defined as follows:
- Set A = [0, 3]
- Set B = [2, 6]

### Step 2: Understand the representation of the sets
The interval [0, 3] means that set A includes all real numbers from 0 to 3, including the endpoints 0 and 3. Similarly, the interval [2, 6] means that set B includes all real numbers from 2 to 6, including the endpoints 2 and 6.

### Step 3: Visualize the sets on a number line
To visualize, we can draw a number line:
- Mark the points 0, 1, 2, 3, 4, 5, and 6.
- Shade the region from 0 to 3 for set A.
- Shade the region from 2 to 6 for set B.

### Step 4: Find the intersection
The intersection of two sets, denoted as A ∩ B, consists of all elements that are common to both sets.

- Set A includes the numbers: 0, 1, 2, 3.
- Set B includes the numbers: 2, 3, 4, 5, 6.

The common elements between these two sets are the numbers from 2 to 3.

### Step 5: Write the intersection in interval notation
Since both endpoints 2 and 3 are included in both sets, the intersection can be expressed as:
- A ∩ B = [2, 3]

### Final Answer
The intersection of sets A and B is:
\[ A \cap B = [2, 3] \]

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