Let `A={x:x inR,xge2}andB={x:x inR,xlt4}` Then `AnnB=`

Options

A. `{x:x inR,2ltxlt4}`
B. `{x:x inR,2lexlt4}`
C. B
D. None of these

Answer

To solve the problem, we need to find the intersection of the two sets \( A \) and \( B \).

### Step-by-Step Solution:

1. **Define Set A**:
Set \( A \) is defined as:
\[ A = \{ x \in \mathbb{R} : x \geq 2 \} \]
This means that set \( A \) contains all real numbers that are greater than or equal to 2.

2. **Define Set B**:
Set \( B \) is defined as:
\[ B = \{ x \in \mathbb{R} : x < 4 \} \]
This means that set \( B \) contains all real numbers that are less than 4.

3. **Visualize the Sets**:
- On a number line, set \( A \) starts at 2 and extends to infinity (2, 3, 4, ...).
- Set \( B \) includes all numbers to the left of 4 (..., 1, 2, 3).

4. **Find the Intersection \( A \cap B \)**:
The intersection of sets \( A \) and \( B \) is the set of all elements that are in both \( A \) and \( B \).
- From set \( A \), we have \( x \geq 2 \).
- From set \( B \), we have \( x < 4 \).
- Therefore, the intersection \( A \cap B \) consists of all \( x \) such that:
\[ 2 \leq x < 4 \]

5. **Express the Intersection in Set Notation**:
We can express the intersection in set-builder notation as:
\[ A \cap B = \{ x \in \mathbb{R} : 2 \leq x < 4 \} \]

### Final Answer:
Thus, the intersection \( A \cap B \) is:
\[ A \cap B = \{ x \in \mathbb{R} : 2 \leq x < 4 \} \]