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

Answer

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

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

### Step 2: Understand the Intervals
Set A includes all real numbers from 0 to 3, including the endpoints 0 and 3.
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
On a number line:
- The interval for Set A (from 0 to 3) will cover the points 0, 1, 2, and 3.
- The interval for Set B (from 2 to 6) will cover the points 2, 3, 4, 5, and 6.

### Step 4: Determine the Union of the Sets
The union of two sets A and B, denoted as A ∪ B, includes all elements that are in A, in B, or in both.

- From Set A, we have the elements from 0 to 3.
- From Set B, we have the elements from 2 to 6.

When we combine these two sets, we see that:
- The elements from 0 to 3 (from Set A) and the elements from 2 to 6 (from Set B) together cover all elements from 0 to 6.

### Step 5: Write the Union Set
Thus, the union of sets A and B is:
\[ A \cup B = [0, 6] \]

### Final Answer
The union of the sets A and B is:
\[ A \cup B = [0, 6] \]

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