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

Answer

To find the complement of the set \( A \), denoted as \( A' \), we need to understand the definition of the complement in the context of the real number line.

### Step-by-Step Solution:

1. **Identify the Set \( A \)**:
The set \( A \) is given as \( A = [0, 3] \). This means that \( A \) includes all real numbers \( x \) such that \( 0 \leq x \leq 3 \).

2. **Understand the Complement**:
The complement of a set \( A \), denoted as \( A' \), consists of all elements in the universal set that are not in \( A \). In this case, we consider the universal set to be the set of all real numbers.

3. **Determine the Range of \( A' \)**:
Since \( A \) includes all numbers from \( 0 \) to \( 3 \), the complement \( A' \) will include:
- All numbers less than \( 0 \) (i.e., \( (-\infty, 0) \))
- All numbers greater than \( 3 \) (i.e., \( (3, +\infty) \))

4. **Express the Complement**:
Therefore, we can express the complement \( A' \) as:
\[ A' = (-\infty, 0) \cup (3, +\infty) \]

### Final Answer:
The complement of the set \( A \) is:
\[ A' = (-\infty, 0) \cup (3, +\infty) \]